Recent zbMATH articles in MSC 81https://www.zbmath.org/atom/cc/812022-01-14T13:23:02.489162ZUnknown authorWerkzeugThe fate of Schrodinger's cat. Using math and computers to explore the counterintuitivehttps://www.zbmath.org/1475.000042022-01-14T13:23:02.489162Z"Stein, James D."https://www.zbmath.org/authors/?q=ai:stein.james-d-junDass die meisten Menschen nicht probabilistisch denken können, wird besonders drastisch durch bornierte Impfgegner belegt, die zur Zeit mal wieder lautstark ihre absurden Pseudo-Argumente absondern. Mathematisch betrachtet ist die Wahrscheinlichkeitstheorie (als Unterkategorie der Maßtheorie) allerdings ein reiches und höchst interessantes Gebiet.
Im vorliegenden Büchlein stellt der Autor viele interessante Beispiele wahrscheinlichkeitstheoretischer Probleme ebenso kompetent wie unterhaltsam vor. Elementare Grundbegriffe der Wahrscheinlichkeitsrechnung werden im Anhang vorgestellt. Ansonsten erfordert die Lektüre so gut wie keine mathematischen Vorkenntnisse; daher kann man das Buch allen interessierten Laien als Ferien- oder Feierabendlektüre empfehlen.
Dass Schrödingers (nicht Schrodingers!) Katze für den Titel herhalten musste, offenbar zur Steigerung der Verkaufszahlen und der Aufmerksamkeit potentieller Leser, ist allerdings bedauerlich. Ähnlich wie der in der Chaostheorie leider oft bemühte ``Schmetterlingseffekt'' zeigt dies, dass Metaphern Glückssache sind.
Reviewer: Jürgen Appell (Würzburg)Toward a formal foundation for time travel in stories and gameshttps://www.zbmath.org/1475.000052022-01-14T13:23:02.489162Z"Helvensteijn, Michiel"https://www.zbmath.org/authors/?q=ai:helvensteijn.michiel"Arbab, Farhad"https://www.zbmath.org/authors/?q=ai:arbab.farhadSummary: Time-travel is a popular topic not only in science fiction, but in physics as well, especially when it concerns the notion of ``changing the past''. It turns out that if time-travel exists, it will follow certain logical rules. In this paper we apply the tools of discrete mathematics to two such sets of rules from theoretical physics: the Novikov Self Consistency Principle and the Many Worlds Interpretation of quantum mechanics. Using temporal logic, we can encode the dynamics of a time-travel story or game, and model-check them for adherence to the rules. We also present the first ever game-engine following these rules, allowing the development of technically accurate time-travel games.
For the entire collection see [Zbl 1460.68002].Editorial: Non-Hermitian quantum mechanicshttps://www.zbmath.org/1475.000532022-01-14T13:23:02.489162ZFrom the text: The present special section tries to capture an essential part of the wide spectrum of the study of non-Hermitian quantum mechanics. It contains a paper on computation of the resonance poles in nuclides, several papers on non-Hermitian topological matters, two papers on non-Hermitian many-body systems, as well as a paper on an experiment; they should all indicate entry paths to further developments of non-Hermitian quantum mechanics.Prefacehttps://www.zbmath.org/1475.000932022-01-14T13:23:02.489162ZFrom the text: This special issue of ``Reviews in Mathematical Physics'' contains refereed papers authored by some of the invited speakers to the QMath14 conference held at the Department of Mathematics, Aarhus University, Denmark in the period of August 12--16, 2019.Prefacehttps://www.zbmath.org/1475.000962022-01-14T13:23:02.489162ZFrom the text: In the last few years, we have witnessed an increasing interest in bridging two important research areas that fundamentally changed our way and abilities of processing information, namely machine learning and quantum computation.
This special issue is dedicated to this event, which was held in Verona on 6--8 November 2017 under the name of QTML 2017 -- 1st workshop on quantum
techniques in machine learning.Special issue ``Quantum computation complexity theory and quantum network theory'' (preface)https://www.zbmath.org/1475.001092022-01-14T13:23:02.489162ZFrom the text: The quantum computation complexity theory and quantum network theory, is at the heart of quantum theory and quantum technology, aiming at providing the chief theoretical foundation for quantum computing and quantum computer. The sixth postgraduate international summer school of Zhejiang university for quantum computation complexity theory and quantum network theory, from July 6 to August 2, 2020, has been successfully held.Recent developments of mathematical methods in theoretical particle physics -- in memory of Tohru Eguchi. I.https://www.zbmath.org/1475.001572022-01-14T13:23:02.489162ZFrom the text: This special section is dedicated to the memory of the late Professor Tohru Eguchi. For Part II see [Zbl 1475.00158].Recent developments of mathematical methods in theoretical particle physics -- in memory of Tohru Eguchi. IIhttps://www.zbmath.org/1475.001582022-01-14T13:23:02.489162ZFrom the text: This special section is dedicated to the memory of the late professor Tohru Eguchi. For Part I see [Zbl 1475.00157].Quantum variance for Eisenstein serieshttps://www.zbmath.org/1475.110942022-01-14T13:23:02.489162Z"Huang, Bingrong"https://www.zbmath.org/authors/?q=ai:huang.bingrongSummary: In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on \(\mathrm{PSL}_2(\mathbb{Z}) \setminus \mathbb{H}\). The resulting quadratic form is compared with the classical variance and the quantum variance for cusp forms. They coincide after inserting certain subtle arithmetic factors, including the central values of certain \(L\)-functions.Entangleability of coneshttps://www.zbmath.org/1475.150342022-01-14T13:23:02.489162Z"Aubrun, Guillaume"https://www.zbmath.org/authors/?q=ai:aubrun.guillaume"Lami, Ludovico"https://www.zbmath.org/authors/?q=ai:lami.ludovico"Palazuelos, Carlos"https://www.zbmath.org/authors/?q=ai:palazuelos.carlos"Plávala, Martin"https://www.zbmath.org/authors/?q=ai:plavala.martinGiven two finite-dimensional cones \(\mathcal{C}_{1}, \mathcal{C}_{2},\) one can define ``from the inside'' their minimal tensor product \(\mathcal{C}_{1} \bigodot\mathcal{C}_{2}\) or ``from outside'' their maximal tensor product \(\mathcal{C}_{1}\circledast \mathcal{C}_{2}.\) Notice that \(\mathcal{C}_{1} \bigodot\mathcal{C}_{2}\subseteq \mathcal{C}_{1}\circledast\mathcal{C}_{2}\) and \(\mathcal{C}_{1}\circledast\mathcal{C}_{2}= (\mathcal{C}^{*}_{1}\bigodot\mathcal{C}^{*}_{2})^{*}.\) Here, \(\mathcal{C}^{*}\) is the dual cone to a cone \(\mathcal{C}.\) Along the paper, the authors focus the attention on proper cones i.e. closed convex cones \(\mathcal{C}\) in a finite-dimensional real linear space \(V\) such that both \(\mathcal{C}\bigcap(-\mathcal{C})= {0}, \mathcal{C}-\mathcal{C}= V.\)
A pair of cones \((\mathcal{C}_{1}, \mathcal{C}_{2})\) is said to be nuclear if \(\mathcal{C}_{1} \bigodot\mathcal{C}_{2}= \mathcal{C}_{1}\circledast\mathcal{C}_{2}\) while the pair is said to be entangleable if \(\mathcal{C}_{1} \bigodot\mathcal{C}_{2}\neq \mathcal{C}_{1}\circledast\mathcal{C}_{2}.\) The terminology ``nuclear'' is borrowed from the analogous notion in \(C^{*}\)-algebras, while the concept of entangleability comes from the interpretation of cones in the context of general probabilistic theories (quantum mechanics is a special case). Cones corresponding to quantum mechanics belong to the family \((PSD_{n})_{n\geq1}\), where \(PSD_{n}\) denotes the cone of positive semi-definite matrices of size \(n\times n\) with complex entries. Quantum entanglement is connected with the fact that \((PSD_{m}, PSD_{n}), m, n\geq 2,\) is an entangleable pair.
In the paper, the authors prove a simple and nice characterization of nuclearity conjectured in [\textit{G. P. Barker}, Linear Algebra Appl. 39, 263--291 (1981; Zbl 0467.15002)]. Indeed, a pair of proper cones is nuclear if and only if on of them is classical (see Theorem A). Here, classical means that the cone is isomorphic to \(\mathbb R^{n}_{+},\) or equivalently a cone whose bases are simplices. The proof is based on a geometric property, the kite-square sandwiching, that characterises non-classical cones (see Theorem B). This geometric property involves cones based on two specific planar shapes: the \emph{kite} and the\emph{ blunt square}. In the next step, they show that kite-square sandwichings can be used to produce a certificate of entangleability. Indeed, two auxiliary results deal with the fact that a proper cone is non-classical if and only if it admits a kite-square sandwiching (Theorem B) and if a pair of proper cones admit a kite square-sandwiching, then the pair is entangleable (Theorem C). A generalisation of Theorem A for a finite number of proper cones is also deduced.
As a byproduct of Theorem A, the authors answer a question raised in [\textit{B. Passer} et al., J. Funct. Anal. 274, No. 11, 3197--3253 (2018; Zbl 1422.47021)] in the framework of matrix convex sets.
Reviewer: Francisco Marcellán (Leganes)A graphical calculus for integration over random diagonal unitary matriceshttps://www.zbmath.org/1475.150472022-01-14T13:23:02.489162Z"Nechita, Ion"https://www.zbmath.org/authors/?q=ai:nechita.ion"Singh, Satvik"https://www.zbmath.org/authors/?q=ai:singh.satvikThe authors present a graphical tool to compute the expectation of tensor network diagrams containing two collections of uniformly distributed unitary random vectors on a unit circle. The relevant mathematical tools, both from combinatorics and from graphical expressions for quantum networks, are briefly given in Section 3. The main result is stated in Theorem 4.8 where it is shown the the expectation can be expressed as a summation over diagrams constrained by several different rules of connections among the links replacing the random vectors. A similar statement is presented for the case of real vectors in Theorem 5.5. The remaining parts of the article exploit the applications of the two main relations to bipartite system networks concerning random unitary matrices including the analysis of twirling maps between matrix algebras. In addition, some observations for tripartite system networks are discussed in the application sections.
The paper is written with heavy technicality in mathematics, hence the readers must be familiar with the concepts and the nomenclature used in combinatorics to well understand the analysis in the paper. However, the results and their derivations are well organised and straightforward. For the readers who are not familiar with combinatorics, I suggest, to begin with, the main statement in Section 4, especially with Theorem 4.8. The mathematical background in Section 3 can be used to follow the proof. In the application sections, despite the detailed discussions for the employed examples, there remain several open problems that one can investigate both mathematically and physically. For instance, the generalisation to the networks concerning multipartite matrices, the consideration of the different types of the underlying distribution, or the connection to the physical implementation of the considered networks, remain open.
Reviewer: Fattah Sakuldee (Warszawa)Affinizations and R-matrices for quiver Hecke algebrashttps://www.zbmath.org/1475.160242022-01-14T13:23:02.489162Z"Kashiwara, Masaki"https://www.zbmath.org/authors/?q=ai:kashiwara.masaki"Park, Euiyong"https://www.zbmath.org/authors/?q=ai:park.euiyongThe notion of quiver Hecke algebras (or Khovanov-Lauda-Rouquier algebras) has played an important role in the theory of categorification as it decategorifies to the negative half of the quantum groups. When a quiver Hecke algebra \(R(\beta)\) is symmetric, it enjoys favorable properties, including:
\begin{enumerate}
\item There exists so-called R-matrices, which are special (non-graded) homomorphisms of the form
\[
R_{M_{z}, N_{z'}}: M_{z} \circ N_{z'} \to N_{z'} \circ M_{z}
\]
between the two convolution products of the affinizations \(M_{z}\) and \(N_{z'}\) of \(R(\beta)\)-modules \(M\) and \(N\) with respect to spectral parameters \(z\) and \(z'\), respectively.
\item There exists a quantum affine Schur-Weyl functor between graded module categories, for a set \(J\) of datum.
\[
\mathfrak{F}: \text{Mod}_{gr}(R^J(\beta)) \to \text{Mod}_{gr}(U'_q(\mathfrak{g})).
\]
\end{enumerate}
In this paper, the authors have introduced the notion of affinizations and R-matrices for an arbitrary quiver Hecke algebra. By an affinization of a simple \(R(\beta)\)-module \(\overline{M}\) they now mean a certain pair \((M,z)\) of an \(R(\beta)\)-module \(M\) and an endomorphism \(z:M\to M\) such that \(M/z(M) \simeq \overline{M}\); while an R-matrix for an arbitrary quiver Hecke algebra is now a special homomorphism
\[
r_{\overline{M}, N}: \overline{M} \circ N \to N \circ \overline{M}.
\]
In Proposition~2.10 it is proved that \(r_{\overline{M}, N}\) has similar properties to R-matrices for symmetric quiver Hecke algebras.
Inspired by the quantum affine Schur-Weyl functor, the authors further construct a duality functor
\[
\mathfrak{F}^{\mathcal{D}}: \text{Mod}_{gr}(R(\beta)^\mathcal{D}) \to \text{Mod}_{gr}(R(\beta)^\mathcal{D})
\]
between graded module categories of two (possibly of distinct types) quiver Hecke algebras \(R(\beta)\) and \(R(\beta)^{\mathcal{D}}\), where \(\mathcal{D}\) is the so called duality datum. It is proved in Theorem~4.3 that \(\mathfrak{F}^{\mathcal{D}}\) is a tensor functor sending finite dimensional modules to finite dimensional modules, and is exact if \(R(\beta)^\mathcal{D}\) is of finite type.
In the final sections, the authors provide examples when \((R(\beta), R(\beta)^\mathcal{D})\) is of the following types: \((D_\ell, A_\ell)\), \((C_\ell, A_\ell)\), \((B_{\ell-1}, B_\ell)\) and \((A_{\ell-1}, B_\ell)\).
Reviewer: Chun-Ju Lai (Taipei)Equivariant \(K\)-theory of semi-infinite flag manifolds and the Pieri-Chevalley formulahttps://www.zbmath.org/1475.170242022-01-14T13:23:02.489162Z"Kato, Syu"https://www.zbmath.org/authors/?q=ai:kato.syu"Naito, Satoshi"https://www.zbmath.org/authors/?q=ai:naito.satoshi"Sagaki, Daisuke"https://www.zbmath.org/authors/?q=ai:sagaki.daisukeLet \(G\) be a connected, simply connected and simple algebraic group over \(\mathbb{C}\). Fix a Borel subgroup \(B\), its maximal torus \(H\) and the Weyl group \(W\). Let \(P^+\) denote the set of integral dominant weights. Consider the Grothendieck ring \(K_H(G/B)\) of the category of \(H\)-equivariant coherent sheaves on the flag variety \(G/B\). It has a basis over the Laurent polynomial ring \(K_H(\mathrm{pt})\) given by the the classes \([\mathcal{O}_{X_w}]\) of the structure sheaves of Schubert varieties \(X_w\) for \(w \in W\). The Pieri-Chevalley formula expresses the product \([\mathcal{L}_{\lambda}] [\mathcal{O}_{X_w}]\) in this basis; here \(\lambda \in P^+\) and \(\mathcal{L}_{\lambda} \longrightarrow G/B\) is the line bundle arising from the one-dimensional \(B\)-module of weight \(\lambda\).
\textit{P. Littelmann} and \textit{C. S. Seshadri} [Prog. Math. 210, 155--176 (2003; Zbl 1100.14526)] related the above linear combination to the standard monomial theory for finite-dimensional \(G\)-modules. In more details, for \(\lambda \in P^+\), the simple \(G\)-module \(L(\lambda)\) of highest weight \(\lambda\) has a basis \((p_{\pi})\) indexed by Littelmann-Seshadri paths \(\pi\) of shape \(\lambda\). Let \(\mu \in P^+\) and view \(L(\lambda+\mu)\) as a submodule of the tensor product \(L(\lambda) \otimes L(\mu)\). The standard monomial theory provides a monomial basis \((p_{\pi} p_{\eta})\) of \(L(\lambda+\mu)\), indexed by pairs of Littelmann-Seshadri paths \(\pi\) and \(\eta\) of shapes \(\lambda\) and \(\mu\) respectively, satisfying a certain standard property. Then the linear combination for \([\mathcal{L}_{\lambda}][\mathcal{O}_{X_w}]\) is encoded in the monomial bases of \(V(\lambda+\mu)\) for specific choices of \(\mu\).
Let \(U_q(\mathfrak{g}_{\mathrm{aff}})\) denote the quantum affine algebra associated to the affinization \(\mathfrak{g}_{\mathrm{aff}}\) of the Lie algebra of \(G\), and \(W_{\mathrm{aff}}\) the affine Weyl group, which is a semi-direct product of \(W\) with the integral coweight lattice of \(G\). For \(\lambda \in P^+\) and \(x \in W_{\mathrm{aff}}\), Kashiwara introduced the level zero extremal module \(V(\lambda)\) over \(U_q(\mathfrak{g}_{\mathrm{aff}})\) and its Demazure submodule \(V_x(\lambda)\) over the nilpotent subalgebra \(U_q^-(\mathfrak{g}_{\mathrm{aff}})\), and equipped both modules with compatible crystal structure. The recent works [\textit{M. Ishii} et al., Adv. Math. 290, 967--1009 (2016; Zbl 1387.17028)] and [\textit{S. Naito} and \textit{D. Sagaki}, Math. Z. 283, No. 3--4, 937--978 (2016; Zbl 1395.17029)] described the crystal structure in terms of semi-infinite Littelmann-Seshadri paths.
In the present work the authors generalize the Pieri-Chevalley formula to an ``affine version'' of \(G/B\), the semi-infinite flag manifold \(\mathbf{Q}_G\). For that purpose, the authors establish fundamental results on semi-infinite Schubert varieties \(\mathbf{Q}_G(x)\) indexed by \(x \in W_{\mathrm{aff}}\) (actually one needs to replace the integral coweight lattice by the cone). Notably, for \(\lambda \in P^+\), the structure sheaf \(\mathcal{O}_{\mathbf{Q}_G(x)}\) twisted by the line bundle \(\mathcal{L}_{\lambda}\) has vanishing higher cohomology and its space of global sections is identified with the Demazure submodule \(V_x(-w_0 \lambda)\), where \(w_0\) denotes the longest element in the Weyl group \(W\). These results enable the authors to have a good definition of K-theory of \(\mathbf{Q}_G\), equivariant with respect to the Iwarahori subgroup of \(G(\mathbb{C}[[z]])\). To express \([\mathcal{L}_{\lambda}][\mathcal{O}_{\mathbf{Q}_G(x)}]\) as a linear combination of the classes \([\mathcal{O}_{\mathbf{Q}_G(y)}]\) for \(y \in W_{\mathrm{aff}}\), as in the classical case of Littelmann-Seshadri, the authors develop a standard monomial theory for crystal bases of Demazure modules.
Reviewer: Huafeng Zhang (Villeneuve d'Ascq)Equivariant vector bundles over quantum sphereshttps://www.zbmath.org/1475.170252022-01-14T13:23:02.489162Z"Mudrov, Andrey"https://www.zbmath.org/authors/?q=ai:mudrov.andrey-iIn this paper, the author constructs one sided projective module over the quantized coordinate ring of the even sphere. This can be seen as a extension of the deformation quantization program. The author begins with recalling certain properties of extremal projectors. The pseudo-parabolic subcategory associated with the quantum sphere is studied. Then, a description of vector bundles via invariants of the coideal subalgebra from the quantum symmetric pairs is also given.
Reviewer: Angela Gammella-Mathieu (Metz)PBWD bases and shuffle algebra realizations for \(U_v(L\mathfrak{sl}_n)\), \(U_{v_1,v_2} (L\mathfrak{sl}_n)\), \(U_v (L\mathfrak{sl}(m|n))\) and their integral formshttps://www.zbmath.org/1475.170272022-01-14T13:23:02.489162Z"Tsymbaliuk, Alexander"https://www.zbmath.org/authors/?q=ai:tsymbaliuk.oleksanderThe quantum loop algebras associated to a simple finite dimensional Lie algebra $\mathfrak{g}$ admit two presentations: the Drinfeld-Jimbo realization $U^{DJ}_v(L\mathfrak{g})$ and the Drinfeld realization $U_v(L\mathfrak{g})$ (cf. [\textit{V. G. Drinfel'd}, Sov. Math., Dokl. 36, No. 2, 212--216 (1988; Zbl 0667.16004); translation from Dokl. Akad. Nauk SSSR 269, 13--17 (1987)]).
The central aim of the paper under review is constructing a family of PBWD (Poincaré-Birkhoff-Witt-Drinfeld) bases for the quantum loop algebras $U_v(L\mathfrak{sl}_n)$, $U_{v_1,v_2}(L\mathfrak{sl}n)$, and $U_v(L\mathfrak{sl}(m|n))$, in the Drienfeld realization.
Moreover, the author provides a family of PBWD bases for certain integral forms $\mathfrak{U}_v(L\mathfrak{sl}_n)$, $\mathfrak{U}_{v_1,v_2} (L\mathfrak{sl}_n)$, $\mathfrak{U}_v(L\mathfrak{sl}(m|n))$, defined over $\mathbb{C}[v, v^{-1}]$ and $\mathbb{C}[v_1, v_2, v_1^{-1}, v_2^{-1}]$, respectively.
Reviewer: Ilaria Colazzo (Exeter)The low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural moduleshttps://www.zbmath.org/1475.170332022-01-14T13:23:02.489162Z"Ecker, Jill"https://www.zbmath.org/authors/?q=ai:ecker.jill"Schlichenmaier, Martin"https://www.zbmath.org/authors/?q=ai:schlichenmaier.martinThe article under review computes (in a largely elementary fashion) the (algebraic) Lie algebra cohomology spaces \(H^3(\mathfrak{g},\mathfrak{g})\) with values in the adjoint module, for the Witt- and Virasoro Lie algebras \(\mathcal{W}\) and \(\mathcal{V}\) in characteristic zero.
Here \textit{algebraic cohomology} means that the cochain spaces in the computation of the cohomology of these infinite-dimensional Lie algebras consist of all algebraic cochains and not only of the continuous cochains with respect to some topology on \(\mathcal{W}\) and \(\mathcal{V}\). The continuous cohomology (also called Gelfand-Fuchs cohomology) is known, see
[\textit{D. B. Fuks}, Cohomology of infinite-dimensional Lie algebras. Transl. from the Russian by A. B. Sosinskiĭ. New York, NY: Consultants Bureau (1986; Zbl 0667.17005)]. Nowadays, even the algebraic cohomology of vector field Lie algebras on smooth affine algebraic varieties is computed, see
[\textit{B. Hennion} and \textit{M. Kapranov}, ``Gelfand-Fuchs cohomology in algebraic geometry and factorization algebras'', Preprint, \url{arXiv:1811.05032}],
but the case of non-trivial coefficients is open.
The outcome of the (rather tedious) computation is that \(H^3(\mathcal{W}, \mathcal{W})\) is zero, while \(H^3(\mathcal{V},\mathcal{V})\) is 1-dimensional (deduced from \(H^3(\mathcal{W},\mathcal{W})\) via the Hochschild-Serre spectral sequence).
For the entire collection see [Zbl 1460.17002].
Reviewer: Friedrich Wagemann (Nantes)Quantum Langlands duality of representations of \(\mathcal{W}\)-algebrashttps://www.zbmath.org/1475.170412022-01-14T13:23:02.489162Z"Arakawa, Tomoyuki"https://www.zbmath.org/authors/?q=ai:arakawa.tomoyuki"Frenkel, Edward"https://www.zbmath.org/authors/?q=ai:frenkel.edward-vThe main result of the paper under review establishes the duality isomorphisms for certain representations of W-algebras at irrational level. Additionally, the papers proves irreducibility of such representations, identifies their highest weights as W-algebra modules, computes their characters and constructs an analogue of the BGG resolution for these representations. These representation play an essential role in the quantum geometric Langlands program. The proof is based on realization of these representations as the intersection of the kernels of powers of screening operators.
Reviewer: Volodymyr Mazorchuk (Uppsala)Lie subalgebras of differential operators in one variablehttps://www.zbmath.org/1475.170452022-01-14T13:23:02.489162Z"Plaza Martín, F. J."https://www.zbmath.org/authors/?q=ai:plaza-martin.francisco-jose"Tejero Prieto, C."https://www.zbmath.org/authors/?q=ai:tejero-prieto.carlosThe Virasoro algebra is a class of important Lie algebras, which has been widely used in many physics areas and other mathematical branches, such as quantum physics, conformal field theory, Kac-Moody algebras, vertex algebras, and so on. It is well know that the centerless Virasoro algebra is called the Witt algebra.
Let \(\mathrm{Diff}(V)\) be the Lie algebra of differential operators on \(V = \mathbb{C}((z))\), \(\mathbb{C}[[z]]\) or \(V=\mathbb{C}(z)\). In this paper, the authors explicitly describe all Lie algebra homomorphisms from \(\mathrm{sl}(2)\), Witt algebra, and Virasoro algebra to \(\mathrm{Diff}(V)\), such that \(L_0\) acts on V as a first-order differential operator.
Reviewer: Haibo Chen (Shanghai)Some exceptional extensions of Virasoro vertex operator algebrashttps://www.zbmath.org/1475.170472022-01-14T13:23:02.489162Z"Ai, Chunrui"https://www.zbmath.org/authors/?q=ai:ai.chunrui"Dong, Chongying"https://www.zbmath.org/authors/?q=ai:dong.chongying"Lin, Xingjun"https://www.zbmath.org/authors/?q=ai:lin.xingjunIn rational two-dimensional conformal quantum field theory, an important problem is to classify the \(SL(2,\mathbb{Z})\)-invariant conformal-field-theoretic partition functions that can be obtained from the characters of modules for a rational vertex operator algebra \(V\). It is known [\textit{C. Dong}, \textit{X. Lin} and \textit{S.-H. Ng}, Algebra Number Theory 9, No. 9, 2121--2166 (2015; Zbl 1377.17025)] that such partition functions can be obtained from rational extension algebras \(U\supseteq V\). Conversely, one can ask if a partition function obtained from the characters of \(V\)-modules comes from a rational vertex operator algebra extension \(U\).
Physicists have classified the modular-invariant partition functions that can be obtained from the characters of rational Virasoro vertex operator algebras \(L(c_{p,q},0)\) at central charge \(c_{p,q}=1-\frac{6(p-q)^2}{pq}\) for relatively prime integers \(p,q\geq 2\) (see for example the tables in Section 10.7 of [\textit{P. Di Francesco}, \textit{P. Mathieu} and \textit{D. Senechal}, Conformal field theory. New York, NY: Springer (1997; Zbl 0869.53052)]). These partition functions are labeled by ordered pairs of ADE Dynkin diagrams. In the paper under review, the authors construct rational vertex operator algebras \(U\) giving the exceptional modular-invariant partition functions of types \((A_{q-1}, E_6)\) for \(q\equiv 11\,\mathrm{mod}\,12\), \((E_6, A_{p-1})\) for \(p\equiv 1\,\mathrm{mod}\,12\), \((A_{q-1},E_8)\) for \(q\equiv 29\,\mathrm{mod}\,30\), and \((E_8,A_{p-1})\) for \(p\equiv 1\,\mathrm{mod}\,30\). These vertex operator algebras are extensions of \(L(c_{12,q},0)\), \(L(c_{p,12},0)\), \(L(c_{30,q},0)\), and \(L(c_{p,30},0)\), respectively. The authors also prove that the vertex operator algebra structures on these extensions \(U\) of \(L(c_{p,q},0)\) are unique up to isomorphism.
Except for the first case in each of the four series, the authors' vertex operator algebras \(U\) extending \(L(c_{p,q},0)\) are non-unitary (the unitary extensions had already been constructed by two of the authors in [\textit{C. Dong} and \textit{X. Lin}, Commun. Math. Phys. 340, No. 2, 613-637 (2015; Zbl 1371.17025)]). In the paper under review, the authors construct each \(U\) recursively, starting from the first unitary cases, using the vertex operator algebra extensions
\[
L(c_{p+p',p},0)\otimes L(c_{p',p+p'},0)\subseteq\mathcal{U}\otimes L(c_{p',p},0)
\]
obtained in [\textit{M. Bershtein}, \textit{B. Feigin} and \textit{A. Litvinov}, Lett. Math. Phys. 106, No. 1, 29-56 (2016; Zbl 1395.17058)]; here \(\mathcal{U}\) is a lattice vertex algebra with a modified conformal vector. The proof of uniqueness for the vertex operator algebra structure on \(U\) is also inductive.
Reviewer: Robert McRae (Beijing)The logos categorical approach to quantum mechanics. I: Kochen-Specker contextuality and global intensive valuationshttps://www.zbmath.org/1475.180032022-01-14T13:23:02.489162Z"de Ronde, C."https://www.zbmath.org/authors/?q=ai:de-ronde.christian"Massri, C."https://www.zbmath.org/authors/?q=ai:massri.cesarThe first author [``Unscrambling the omelette of quantum contextuality. I: Preexistent properties or measurement outcomes?'', Preprint, \url{arXiv:1606.03967}] argued that there exist two different notions of quantum contextuality within the foundational literature. The first, due to \textit{N. Bohr} [Phys. Rev., II. Ser. 48, 696--702 (1935; Zbl 0012.42701); \textit{A. Einstein} et al., Phys. Rev., II. Ser. 47, 777--780 (1935; Zbl 0012.04201)], is an epistemic notion of contextuality grounding itself in the classical representation of experimental arrangements and the so-called wave-particle duality. The second, related to Kochen-Specker theorem [\textit{S. Kochen} and \textit{E. P. Specker}, J. Math. Mech. 17, 59--87 (1967; Zbl 0156.23302)] is concerned with an ontic questioning about the formalism of the theory and its possible conceptual representation. While Bohrian contexuality is strictly related to our classical image of the world, Kochen-Specker contexuality is genuinely formal statement regarding valuations about the orthodox formalism of quantum mechanics and the limits of its ontological interpretation in terms of definite valued properties.
This paper presents a new categorical approach attempting to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about. In particular, the authors discuss a solution to Kochen-Specker contextuality through the generalization of the meaning of \textit{global valuation}, which has already been addressed in the so-called topos approach to quantum mechanics [\textit{C. J. Isham}, J. Math. Phys. 35, No. 5, 2157--2185 (1994; Zbl 0814.03040); \textit{C. J. Isham} and \textit{J. Butterfield}, Int. J. Theor. Phys. 37, No. 11, 2669--2733 (1998; Zbl 0979.81018); Int. J. Theor. Phys. 38, No. 3, 827--859 (1999; Zbl 1007.81009); \textit{J. Hamilton} et al., Int. J. Theor. Phys. 39, No. 6, 1413--1436 (2000; Zbl 1055.81004); \textit{J. Butterfield} and \textit{C. J. Isham}, Int. J. Theor. Phys. 41, No. 4, 613--639 (2002; Zbl 1021.81002); \textit{C. J. Isham}, Int. J. Theor. Phys. 36, No. 4, 785--814 (1997; Zbl 0881.03039); \textit{A. Döring} and \textit{C. J. Isham}, J. Math. Phys. 49, No. 5, 053515, 25 p. (2008; Zbl 1152.81408); J. Math. Phys. 49, No. 5, 053516, 26 p. (2008; Zbl 1152.81409); J. Math. Phys. 49, No. 5, 053517, 31 p. (2008; Zbl 1152.81410); J. Math. Phys. 49, No. 5, 053518, 29 p. (2008; Zbl 1152.81411)] in terms of \textit{sieve-valued valuations}. The authors present a different solution in terms of \textit{intensive valuations}. While the topos approach is part of the orthodox line of research attempting to bridge the gap between quantum mechanics and the classical worldview, the authors' logos approach takes as a standpoint the formalism of quantum mechanics, stressing the need to develop an objective conceptual representation of physical reality.
Reviewer: Hirokazu Nishimura (Tsukuba)The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond grouphttps://www.zbmath.org/1475.220192022-01-14T13:23:02.489162Z"Cahen, Benjamin"https://www.zbmath.org/authors/?q=ai:cahen.benjaminIn this paper, the problem of constructing a Stratonovich-Weyl correspondence is revisited, by using the complex Weyl calculus on the Fock space. The author starts with recalling the relevant notions and results. Then, he uses the complex Weyl calculus on the Fock space to prove the main theorems. Closed formulas for the symbols of the representation operators are also obtained.
Reviewer: Angela Gammella-Mathieu (Metz)Polyanalytic Toeplitz operators: isomorphisms, symbolic calculus and approximation of Weyl operatorshttps://www.zbmath.org/1475.320052022-01-14T13:23:02.489162Z"Keller, Johannes"https://www.zbmath.org/authors/?q=ai:keller.johannes.1"Luef, Franz"https://www.zbmath.org/authors/?q=ai:luef.franzThe paper is devoted to the investigation of quantization schemes, in particular Toeplitz quantization, associated to polyanalytic functions. Note that the polyanalytic Toeplitz operators naturally appear as the complexification of the localization operators with Hermite function windows, and polyanalytic Bargmann-Fock spaces are precisely the images of the classical modulation spaces under polyanalytic Bargmann transforms. In Section 3, the authors introduce the true polyanalytic Bargmann transforms and the polyanalytic Toeplitz quantization \(\mathcal{T}_k(m)\), with symbol \(m: \mathbb{C}^d \rightarrow \mathbb{C}\), where \(k \in \mathbb{N}^d\) is the degree of polyanalyticity. The main result of Section 4 establishes the isomorphism between different true polyanalytic Sobolev-Fock spaces under the action of certain polyanalytic Toeplitz operator. Section 5 is devoted to an \(\hbar\)-dependent asymptotic symbol calculus for localization operators \(\mathrm{op}^{\varphi_k}_{\mathrm{aw}}(a)\), where the window \(\varphi_k\) is a Hermite function. In particular, the authors show that the commutator of two Hermite localization operators \(\mathrm{op}^{\varphi_k}_{\mathrm{aw}}(a)\) and \(\mathrm{op}^{\varphi_k}_{\mathrm{aw}}(a)\) has the following asymptotic expansion \[\frac{i}{\hbar}\left[\mathrm{op}^{\varphi_k}_{\mathrm{aw}}(a), \mathrm{op}^{\varphi_k}_{\mathrm{aw}}(a) \right] = \mathrm{op}^{\varphi_k}_{\mathrm{aw}}(\{a,b\}) + O(\hbar),\] where \(\{a,b\}\) is the standard Poisson bracket. In Section 6, an asymptotic expansion of complex Weyl quantized operators in terms of polyanalytic Toeplitz operators is considered.
Reviewer: Nikolaj L. Vasilevskij (Ciudad de México)Finite-dimensional irreducible modules of the universal Askey-Wilson algebra at roots of unityhttps://www.zbmath.org/1475.330112022-01-14T13:23:02.489162Z"Huang, Hau-Wen"https://www.zbmath.org/authors/?q=ai:huang.hau-wenIn this paper \(\mathbb{F}\) is an algebraic closed field and \(q\in\mathbb{F}\) is aprimitive \(d\)th root of unity with \(d\not= 1,2,4\). The universal Askey-Wilson algebra \(\Delta_q\) is a unital associative \(\mathbb{F}\)-algebra generated by \(A,B,C\) and relations asserting that each of \[A+\frac{qBC-q^{-1}CB}{q^2-q^{-2}},\ B+\frac{qCA-q^{-1}AC}{q^2-q^{-2}},\ B+\frac{qAB-q^{-1}BA}{q^2-q^{-2}},\] is central in \(\Delta_q\) (cf. [\textit{P. Terwilliger}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 069, 24 p. (2011; Zbl 1244.33015)]).
Setting \[\hat{d}=\begin{cases}d &\text{ if }d\text{ is odd},\\ d/2 &\text{ if }d\text{ is even}.\end{cases}\] the main result is given as
\textbf{Theorem 1.2} If \(V\) is a finite-dimensional irreducible \(\Delta_q\)-module, then the dimension of \(V\) is less than or equal to \(\hat{d}\).
\vskip0.3cm Here, given any nonzero \(a,b,c\in\mathbb{F}\) and any integer \(n\geq 0\), an \((n+1)\) dimensional \(\Delta_q\)-module \(V_n(a,b,c)\) is constructed as in [\textit{H.-W. Huang}, Commun. Math. Phys. 340, No. 3, 959--984 (2015; Zbl 1331.33036)]. It is irreducible if and only if \(0\leq n\leq d-1\) and \[abc,a^{-1}bc,ab^{-1}c,abc^{-1}\not\in \{q^{2i-n-1}\mid i=1,2,\ldots,n\}.\]
The layout of the paper is as follows:
\S1. Introduction
\S2. Preliminaries
\S3. The \(q\)-Racah sequences
\S4. The decomposition of finite-diminsional irreduciible \(\Delta_q\)-modules
\S5. The operator associated with \(q\)-Racah polynomials
Proof of Theorem 1.2
References (32 items)
Reviewer: Marcel G. de Bruin (Heemstede)Maximal speed of quantum propagationhttps://www.zbmath.org/1475.353012022-01-14T13:23:02.489162Z"Arbunich, J."https://www.zbmath.org/authors/?q=ai:arbunich.jack"Pusateri, F."https://www.zbmath.org/authors/?q=ai:pusateri.fabio"Sigal, I. M."https://www.zbmath.org/authors/?q=ai:sigal.israel-michael"Soffer, A."https://www.zbmath.org/authors/?q=ai:soffer.avrahamThe authors give a gentle introduction to the work that has been done in recently published papers regarding maximal propagation speed bound. The most concern of the paper is to show in a simple and mathematical way how to define and proove the general values of constants that would work, especially for Kato's potentials. However, the paper shows extraordinary mathematical precision in the use of concepts and proofs. An observation of mine would be that this paper gives even a practical guide on how to look for MPS bounds and how to theoretically use them in quantum information theory as a general consequence.
Reviewer: Mevludin Licina (Sarajevo)On dispersion managed nonlinear Schrödinger equations with lumped amplificationhttps://www.zbmath.org/1475.353122022-01-14T13:23:02.489162Z"Choi, Mi-Ran"https://www.zbmath.org/authors/?q=ai:choi.mi-ran"Kang, Younghoon"https://www.zbmath.org/authors/?q=ai:kang.younghoon"Lee, Young-Ran"https://www.zbmath.org/authors/?q=ai:lee.young-ranSummary: We show the global well-posedness of the nonlinear Schrödinger equation with periodically varying coefficients and a small parameter \(\varepsilon > 0\), which is used in optical-fiber communications. We also prove that the solutions converge to the solution for the Gabitov-Turitsyn or averaged equation as \(\varepsilon\) tends to zero.
{\copyright 2021 American Institute of Physics}Direct methods for pseudo-relativistic Schrödinger operatorshttps://www.zbmath.org/1475.353142022-01-14T13:23:02.489162Z"Dai, Wei"https://www.zbmath.org/authors/?q=ai:dai.wei.4"Qin, Guolin"https://www.zbmath.org/authors/?q=ai:qin.guolin"Wu, Dan"https://www.zbmath.org/authors/?q=ai:wu.danSummary: In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators \((- \Delta +m^2)^s\) with \(s \in (0,1)\) and mass \(m>0\). As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators \((- \Delta +m^2)^s\) in bounded or unbounded domains with certain geometrical structures (e.g., coercive epigraph and epigraph), including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi-type nonlinearities. When \(m=0\) and \(s=1\), equations with De Giorgi-type nonlinearities are related to De Giorgi conjecture connected with minimal surfaces and the scalar Ginzburg-Landau functional associated to harmonic map.Almost sure well-posedness for the cubic nonlinear Schrödinger equation in the super-critical regime on \(\mathbb{T}^d\), \(d\geq 3\)https://www.zbmath.org/1475.353242022-01-14T13:23:02.489162Z"Yue, Haitian"https://www.zbmath.org/authors/?q=ai:yue.haitianSummary: In this paper we prove almost sure local (in time) well-posedness in both adapted atomic spaces and Fourier restriction spaces for the periodic cubic nonlinear Schrödinger equation on \(\mathbb{T}^d\) \((d\geq 3)\) in the super-critical regime.On the geometric structures of transmission eigenfunctions with a conductive boundary condition and applicationshttps://www.zbmath.org/1475.353282022-01-14T13:23:02.489162Z"Diao, Huaian"https://www.zbmath.org/authors/?q=ai:diao.huaian"Cao, Xinlin"https://www.zbmath.org/authors/?q=ai:cao.xinlin"Liu, Hongyu"https://www.zbmath.org/authors/?q=ai:liu.hongyuSummary: This paper is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [\textit{E. Blåsten} and \textit{H. Liu}, J. Funct. Anal. 273, No. 11, 3616--3632 (2017; Zbl 1387.35437)]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than \(\pi\). We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in [loc. cit.] as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not \(\pi\) when the conductive transmission eigenfunctions satisfy certain Herglotz functions approximation properties. That means, as long as the corner singularity is not degenerate, the vanishing property holds if the underlying conductive transmission eigenfunctions can be approximated by a sequence of Herglotz functions under mild approximation rates. Third, the regularity requirements on the interior transmission eigenfunctions in [loc. cit.] are significantly relaxed in the present study for the conductive transmission eigenfunctions. In order to establish the geometric properties for the conductive transmission eigenfunctions, we develop technically new methods and the corresponding analysis is much more complicated than that in [loc. cit.]. Finally, as an interesting and practical application of the obtained geometric results, we establish a unique recovery result for the inverse problem associated with the transverse electromagnetic scattering by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductive parameter.Mean field limit for Coulomb-type flowshttps://www.zbmath.org/1475.353412022-01-14T13:23:02.489162Z"Serfaty, Sylvia"https://www.zbmath.org/authors/?q=ai:serfaty.sylviaThe author establishes the mean field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-Coulombic Riesz potential. This task is achieved in arbitrary dimensions, for the first time to the best of my knowledge.
The proof is based on a modulated energy method using a Coulomb or Riesz distance, assuming that the solutions of the limiting equation are regular enough. The method can handle the addition of a regular interaction kernel and applies also to conservative and mixed flows.
In the appendix, written together with Mitia Duerinckx, the mean field convergence is also proved for the solutions to Newton's law with Coulomb or Riesz interaction in the monokinetic case to solutions of an Euler-Poisson type system.
Reviewer: Dmitry Pelinovsky (Hamilton)A note on the Gaffney Laplacian on infinite metric graphshttps://www.zbmath.org/1475.353742022-01-14T13:23:02.489162Z"Kostenko, Aleksey"https://www.zbmath.org/authors/?q=ai:kostenko.aleksey-s"Nicolussi, Noema"https://www.zbmath.org/authors/?q=ai:nicolussi.noemaSummary: We show that the deficiency indices of the minimal Gaffney Laplacian on an infinite locally finite metric graph are equal to the number of finite volume graph ends. Moreover, we provide criteria, formulated in terms of finite volume graph ends, for the Gaffney Laplacian to be closed.Frequency dependence of Hölder continuity for quasiperiodic Schrödinger operatorshttps://www.zbmath.org/1475.370302022-01-14T13:23:02.489162Z"Munger, Paul E."https://www.zbmath.org/authors/?q=ai:munger.paul-eSummary: We study the Hölder exponent of the density of states measure for discrete Schrödinger operators with potential of the form \(V(n) = \lambda(\lfloor (n+1)\beta \rfloor - \lfloor n\beta \rfloor)\), with \(\lambda\) large, and conclude that for almost all values of \(\beta\), the density of states measure is not Hölder continuous.Bethe subalgebras in braided Yangians and Gaudin-type modelshttps://www.zbmath.org/1475.370632022-01-14T13:23:02.489162Z"Gurevich, Dimitri"https://www.zbmath.org/authors/?q=ai:gurevich.dmitrii-i"Saponov, Pavel"https://www.zbmath.org/authors/?q=ai:saponov.pavel-a"Slinkin, Alexey"https://www.zbmath.org/authors/?q=ai:slinkin.alexeyA braided Yangian of reflection type, \(\mathbf{Y}(R)\), is a unital associative algebra generated from
\[
R_1(u,v)L_1(u)R_1L_1(v)= L_1(v)R_1L_1(u)R_1(u,v).
\]
This was studied in [the first and the second author, J. Geom. Phys. 138, 124--143 (2019; Zbl 1414.81136)], where also the quantum counterparts of elementary symmetric polynomials were introduced.
The purpose of this article is to prove that such polynomials commute with each other and generate a commutative Bethe subalgebra.
As an application, a Gaudin-type model based on a method of \textit{D. V. Talalaev} [Funct. Anal. Appl. 40, No. 1, 73--77 (2006; Zbl 1111.82015); translation from Funkts. Anal. Prilozh. 40, No. 1, 86--91 (2006)] is proposed.
Reviewer: Kazuhiro Hikami (Fukuoka)Topological $T$-duality for twisted torihttps://www.zbmath.org/1475.460552022-01-14T13:23:02.489162Z"Aschieri, Paolo"https://www.zbmath.org/authors/?q=ai:aschieri.paolo"Szabo, Richard J."https://www.zbmath.org/authors/?q=ai:szabo.richard-jSummary: We apply the \(C^*\)-algebraic formalism of topological $T$-duality due to \textit{V. Mathai} and \textit{J. Rosenberg} [Commun. Math. Phys. 253, No. 3, 705--721 (2005; Zbl 1078.58006)] to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the $T$-duals starting from a commutative \(C^*\)-algebra with an action of \(\mathbb{R}^n\). We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical $T$-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier-Douady classes. We prove that any such solvmanifold has a topological $T$-dual given by a \(C^*\)-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these \(C^*\)-algebras rigorously describe the $T$-folds from non-geometric string theory.A normalized solitary wave solution of the Maxwell-Dirac equationshttps://www.zbmath.org/1475.490602022-01-14T13:23:02.489162Z"Nolasco, Margherita"https://www.zbmath.org/authors/?q=ai:nolasco.margheritaSummary: We prove the existence of a \(L^2\)-normalized solitary wave solution for the Maxwell-Dirac equations in (3+1)-Minkowski space. In addition, for the Coulomb-Dirac model, describing fermions with attractive Coulomb interactions in the mean-field limit, we prove the existence of the (positive) energy minimizer.Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifoldshttps://www.zbmath.org/1475.530752022-01-14T13:23:02.489162Z"Murro, Simone"https://www.zbmath.org/authors/?q=ai:murro.simone"Volpe, Daniele"https://www.zbmath.org/authors/?q=ai:volpe.danieleSymmetric hyperbolic systems are an important class of first-order linear differential operators acting on sections of vector bundles on Lorentzian manifolds. Two of the most important examples of symmetric hyperbolic systems are given by the classical Dirac operator and the geometric wave operator.
In the paper the authors introduce a geometric process, via a family of intertwining operators, to compare the solutions of different symmetric hyperbolic systems over (possibily different) globally hyperbolic manifolds. By fixing a suitable parameter, they prove that the resulting intertwining operator preserves Hermitian forms naturally defined on the space of homogeneous solutions. As an application, they study the action of the intertwining operators in the context of algebraic quantum field theory. In particular, they obtain a new geometric proof for the existence of the so-called Hadamard states on globally hyperbolic manifolds.
Reviewer: Anna Fino (Torino)Mayer-Vietoris property for relative symplectic cohomologyhttps://www.zbmath.org/1475.530982022-01-14T13:23:02.489162Z"Varolgunes, Umut"https://www.zbmath.org/authors/?q=ai:varolgunes.umutThe article under review is concerned with the construction of a symplectic invariant on closed symplectic manifolds, called relative symplectic cohomology, which is based on Hamiltonian Floer theory. Explicitly, denote by \((M, \omega)\) a symplectic manifold, \(K \subset M\) a compact subset, and \(\Lambda_{\geq 0}\) the Novikov ring defined as follows,
\[
\Lambda_{\geq 0} = \left\{ \sum_{i \in \mathbb N} a_i T^{\alpha_i} \, \bigg| \, a_i \in \mathbb Q, \, \alpha_i \in \mathbb R_{\geq 0}, \, \,\mbox{ where }a_i \to \infty\text{ as }i \to \infty \right\}.
\]
Similarly, \(\Lambda_{>0}\) is an ideal of \(\Lambda_{\geq 0}\) with all exponents \(\alpha_i>0\). Relative symplectic cohomology, denoted by \(\mathrm{SH}_{M}(K)\) is a graded \(\Lambda_{\geq 0}\)-module that has a certain sheaf-like properties, for instance, the global section \(\mathrm{SH}_M(M) = H(M, \mathbb{Z}) \otimes_{\mathbb{Z}} \Lambda_{>0}\), the empty set \(\mathrm{SH}_{M}(\emptyset) = 0\), and for any \(K' \subset K\), there exists a restriction map
\[
\mathrm{res}^{K}_{K'}: \mathrm{SH}_M(K) \to \mathrm{SH}_M(K').
\]
More importantly, \(\mathrm{SH}_M(\cdot)\) satisfies the following Mayer-Vietoris property,
\[
\begin{tikzcd}
\mathrm{SH}_M(K_1 \cup K_2) \rar \dar["[1\text{]}" ']& \mathrm{SH}_M(K_1) \oplus \mathrm{SH}_M(K_2) \dlar \\
\mathrm{SH}_M(K_1 \cap K_2) &
\end{tikzcd}
\]
if \(K_1\) and \(K_2\) are compact domains with boundaries in \(M\) and satisfy some topological constraint, for instance, \(\partial K_1 \cap \partial K_2 = \emptyset\) when \(\dim(M) =2\). Finally, the importance of \(\mathrm{SH}_M(K)\) in terms of symplectic geometry is that it can be used to detect the displaceability (by a Hamiltonian diffeomorphism) of \(K\) in \(M\), which is a fundamental question in symplectic geometry. Namely, if \(K\) is displaceable, then \(\mathrm{SH}_M(K) \otimes_{\Lambda_{\geq 0}} \Lambda = 0\).
The construction of \(\mathrm{SH}_M(K)\) starts from a certain increasing family of Hamiltonian functions \(\{H_i\}_{i \in \mathbb N}\) that approximates an indicator function of \(K\), that is,
\[
H_\infty = \begin{cases} 0 \,\,& \mbox{ on }K \\
+\infty \,\, & \mbox{ on }M \backslash K. \end{cases}
\]
Then \(\mathrm{SH}_M(K)\) is defined as the cohomology of a certain (double) limit of the truncated (at level \(r \geq 0\)) Hamiltonian Floer cochain complex denoted by \(\mathrm{CF}(H_i) \otimes_{\Lambda_{\geq 0}} \Lambda_{[0,r)}\) where \(\Lambda_{[0,r)} : = \Lambda_{\geq 0}/T^r \Lambda_{\geq 0}\). The first (direct) limit is taken from the Floer continuation map
\[
\mathrm{CF}(H_i) \otimes_{\Lambda_{\geq 0}} \Lambda_{[0,r)} \to\mathrm{CF}(H_{i+1}) \otimes_{\Lambda_{\geq 0}} \Lambda_{[0,r)}
\]
induced via a (in fact, any) monotone homotopy from \(H_i\) to \(H_{i+1}\), and the second (inverse) limit is taken over \(r \in \mathbb R_{\geq 0}\) induced from the natural map \(\Lambda_{[0,s)} \to \Lambda_{[0,r)}\) when \(r \leq s\), namely, the completion of a \(\Lambda_{\geq 0}\)-module with respect to the filtration given by \(\{T^r\Lambda_{\geq 0}\}_{r \geq 0}\). The verifications of the well-definedness of \(\mathrm{SH}_M(K)\) as well as its properties can be neatly phrased in the language of cubes and its related algebraic operators that encode higher homotopy relations.
The construction above can be regarded as an analogue of the classical symplectic (co)homology of domains in an open symplectic manifold which was invented in [\textit{C. Viterbo}, Geom. Funct. Anal. 9, No. 5, 985--1033 (1999, Zbl 0954.57015); \textit{K. Cieliebak} et al., Math. Z. 218, No. 1, 103--122 (1995; Zbl 0869.58011)].
Reviewer: Jun Zhang (Montréal)Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantizationhttps://www.zbmath.org/1475.531002022-01-14T13:23:02.489162Z"Miti, Antonio Michele"https://www.zbmath.org/authors/?q=ai:miti.antonio-michele"Spera, Mauro"https://www.zbmath.org/authors/?q=ai:spera.mauroThe HOMFLYPT polynomial \(P=P(\alpha,z)\) is an \textit{ambient isotopy} invariant of links defined by the \textit{skein} relation and a natural normalization. The paper under review uses the Maslov-Hörmander type techniques in order to obtain a new interpretation of the HOMFLYPT (particularly the Conway and the Jones) polynomial as a WKB-wave function through the geometric quantization of the Brylinski manifold of singular knots and links. Another main tool is the surgery via ``figure of eight'' knots. More precisely, the coefficient \(\alpha\) is a phase factor related to the helicity of a standard ``eight-figure'' while \(z\) comes from accounting for the variation of the number of components of a link.
Reviewer: Mircea Crâşmăreanu (Iaşi)Nonconstant hexagon relations and their cohomologyhttps://www.zbmath.org/1475.570422022-01-14T13:23:02.489162Z"Korepanov, Igor G."https://www.zbmath.org/authors/?q=ai:korepanov.igor-gThe famous Pachner moves relate different triangulations of a (PL) manifold. For definiteness, let us focus on the case of 4-manifolds. There is a standard triangulation of the 4-dimensional sphere: use the boundary of a 5-simplex, \(\partial \Delta^5\). There are various ways to divide this sphere into two hemispheres. The different choices parameterize the different 4-dimensional Pachner moves. Specifically, to apply a Pachner move to a triangulated 4-manifold \(M^4\), you select some 4-simplices in \(M^4\) which meet according to the combinators of a hemisphere in \(\partial \Delta^5\), and then you replace your selected hemisphere with the other hemisphere in \(\partial \Delta^5\).
The ``hexagon'' in the title of this paper is the hexagon whose vertices are the six individual 4-simplices in \(\partial \Delta^5\). Hexagon cohomology is a cohomology theory about the combinatorics of 4-dimensional Pachner moves which, the author of this paper hopes, will be related to interesting invariants of 4-manifolds; it is also related, unexpectedly, to four-dimensional free fermions. Hexagon cohomology, and the analogous pentagon cohomology of 3-dimensional Pachner moves, generalize the cohomology theories coming from quandles and Yang-Baxter relations which do provide refined topological invariants. As with those other theories, hexagon cohomology depends on a choice of labels or parameters, which may or may not be constant. Hence the ``nonconstant'' in the title of this paper.
Reviewer: Theo Johnson-Freyd (Waterloo)Supersymmetrization: AKSZ and beyond?https://www.zbmath.org/1475.580042022-01-14T13:23:02.489162Z"Salnikov, V."https://www.zbmath.org/authors/?q=ai:salnikov.vsevolod|salnikov.v-d|salnikov.vladimir|salnikov.v-n.1|salnikov.valeriyThis paper builds generalizations of supersymmetric sigma models in the framework of multigraded geometry. This includes a multigraded extension of the Aleksandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) approach to the problem of supersymmetrization, and a multigraded version of the Kotov-Strobl Q-bundle formalism. Applications are given to the graded Poisson sigma model and to the super Chern-Simons theory.
Reviewer: Nicolas Privault (Singapore)Parabolic Anderson model with rough or critical Gaussian noisehttps://www.zbmath.org/1475.601132022-01-14T13:23:02.489162Z"Chen, Xia"https://www.zbmath.org/authors/?q=ai:chen.xia.1|chen.xiaAuthor's abstract: This paper considers the parabolic Anderson equation \[\frac{\partial u}{\partial t} = \frac{1}{2}\Delta u+u\frac{\partial^{d+1}W^H}{\partial t\partial x_1\ldots\partial x_d}\] generated by a \((d + 1)\)-dimensional fractional noise with the Hurst parameter \(\mathbf{H} = (H_0,H_1,\ldots,H_d),\) where \(W^H\) is the formal derivative of a fractional Brownian sheet. The existence/uniqueness, Feynman-Kac's moment formula and the precise intermittency exponents are formulated in the case when some of \( H_1,\cdots,H_d\) are less than one half, and in the case when the Dalang's condition \(d-\sum_{k=1}^n H_j<1\) is replaced by \(d- \sum_{k=1}^n H_j=1\). Some partial result is achieved for the case when \(H_0 < 1/2\) which brings insight on what to expect as the Gaussian noise is rough in time.
Reviewer: Nasir N. Ganikhodjaev (Tashkent)A statistical analysis of luckhttps://www.zbmath.org/1475.620822022-01-14T13:23:02.489162Z"Wilhelm, Isaac"https://www.zbmath.org/authors/?q=ai:wilhelm.isaacSummary: A modal analysis of luck, due to Duncan Pritchard, has become quite popular in recent years. There are many reasons to like Pritchard's analysis, but at least two compelling problems have been identified. So I propose an alternative analysis of luck based on the laws of statistical mechanics. The statistical analysis avoids the two problems facing Pritchard's analysis, and it has many other attractive features.Mathematical models and numerical methods for spinor Bose-Einstein condensates.https://www.zbmath.org/1475.650642022-01-14T13:23:02.489162Z"Bao, Weizhu"https://www.zbmath.org/authors/?q=ai:bao.weizhu"Cai, Yongyong"https://www.zbmath.org/authors/?q=ai:cai.yongyongSummary: In this paper, we systematically review mathematical models, theories and numerical methods for ground states and dynamics of spinor Bose-Einstein condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We start with a pseudo spin-1/2 BEC system with/without an internal atomic Josephson junction and spin-orbit coupling including (i) existence and uniqueness as well as non-existence of ground states under different parameter regimes, (ii) ground state structures under different limiting parameter regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical methods for computing ground states and dynamics. Then we extend these results to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems and/or general spin-\(F\) (\(F \geq 3\)) BEC are discussed.Error estimates for a class of energy- and Hamiltonian-preserving local discontinuous Galerkin methods for the Klein-Gordon-Schrödinger equationshttps://www.zbmath.org/1475.650972022-01-14T13:23:02.489162Z"Yang, He"https://www.zbmath.org/authors/?q=ai:yang.heSummary: The Klein-Gordon-Schrödinger (KGS) equations are classical models to describe the interaction between conservative scalar nucleons and neutral scalar mesons through Yukawa coupling. In this paper, we propose local discontinuous Galerkin (LDG) methods to solve the KGS equations. The methods involve a Crank-Nicholson time discretization for the Schrödinger equation part, a Crank-Nicholson leap frog method in time for the Klein-Gordon equation part, and local discontinuous Galerkin methods in space. Our designed numerical methods have high-order convergence rate, and energy- and Hamiltonian-preserving properties. We present the proofs of such conservation properties for both semi-discrete and fully-discrete schemes. We also establish optimal error estimates of the semi-discrete methods for the linearized KGS equations and the fully discrete methods for the KGS equations. The analysis can be extended to LDG methods for the nonlinear Klein-Gordon or Schrödinger equation, and the KGS equations in higher spatial dimensions. Several numerical tests are presented to verify some of our theoretical findings.A preconditioned conjugated gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via kernel truncation method for dipole-dipole interaction evaluationhttps://www.zbmath.org/1475.651422022-01-14T13:23:02.489162Z"Antoine, Xavier"https://www.zbmath.org/authors/?q=ai:antoine.xavier"Tang, Qinglin"https://www.zbmath.org/authors/?q=ai:tang.qinglin"Zhang, Yong"https://www.zbmath.org/authors/?q=ai:zhang.yong.2Summary: In this paper, we propose an efficient and accurate method to compute the ground state of 2D/3D rotating dipolar BEC by incorporating the Kernel Truncation Method (KTM) for Dipole-Dipole Interaction (DDI) evaluation into the newly-developed Preconditioned Conjugate Gradient (PCG) method [\textit{X. Antoine} et al., J. Comput. Phys. 343, 92--109 (2017; Zbl 1380.81496)]. Adaptation details of KTM and PCG, including multidimensional discrete convolution acceleration for KTM, choice of the preconditioners in PCG, are provided. The performance of our method is confirmed with extensive numerical tests, with emphasis on spectral accuracy of KTM and efficiency of ground state computation with PCG. Application of our method shows some interesting vortex lattice patterns in 2D and 3D respectively.A hybrid method for computing the Schrödinger equations with periodic potential with band-crossings in the momentum spacehttps://www.zbmath.org/1475.651432022-01-14T13:23:02.489162Z"Chai, Lihui"https://www.zbmath.org/authors/?q=ai:chai.lihui"Jin, Shi"https://www.zbmath.org/authors/?q=ai:jin.shi"Markowich, Peter A."https://www.zbmath.org/authors/?q=ai:markowich.peter-alexanderSummary: We propose a hybrid method which combines the Bloch decomposition-based time splitting (BDTS) method and the Gaussian beam method to simulate the Schrödinger equation with periodic potentials in the case of band-crossings. With the help of the Bloch transformation, we develop a Bloch decomposition-based Gaussian beam (BDGB) approximation in the momentum space to solve the Schrödinger equation. Around the band-crossing a BDTS method is used to capture the inter-band transitions, and away from the crossing, a BDGB method is applied in order to improve the efficiency. Numerical results show that this method can capture the inter-band transitions accurately with a computational cost much lower than the direct solver. We also compare the Schrödinger equation with its Dirac approximation, and numerically show that, as the rescaled Planck number \(\varepsilon \rightarrow 0\), the Schrödinger equation converges to the Dirac equations when the external potential is zero or small, but for general external potentials there is an \(\mathcal{O}(1)\) difference between the solutions of the Schrödinger equation and its Dirac approximation.A mortar spectral element method for full-potential electronic structure calculationshttps://www.zbmath.org/1475.651822022-01-14T13:23:02.489162Z"Guo, Yichen"https://www.zbmath.org/authors/?q=ai:guo.yichen"Jia, Lueling"https://www.zbmath.org/authors/?q=ai:jia.lueling"Chen, Huajie"https://www.zbmath.org/authors/?q=ai:chen.huajie"Li, Huiyuan"https://www.zbmath.org/authors/?q=ai:li.huiyuan"Zhang, Zhimin"https://www.zbmath.org/authors/?q=ai:zhang.zhiminSummary: In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent work of
\textit{H. Li} and \textit{Z. Zhang} [SIAM J. Sci. Comput. 39, No. 1, A114--A140 (2017; Zbl 1355.65150)], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without nuclei. A mortar technique is applied to patch the different discretizations. Numerical experiments are carried out to demonstrate the efficiency of our scheme, especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulomb singularities.Hadamard-free circuits expose the structure of the Clifford grouphttps://www.zbmath.org/1475.681322022-01-14T13:23:02.489162Z"Bravyi, Sergey"https://www.zbmath.org/authors/?q=ai:bravyi.sergey-b"Maslov, Dmitri"https://www.zbmath.org/authors/?q=ai:maslov.dmitriEditorial remark: No review copy delivered.Mathematical optics. Classical, quantum, and computational methodshttps://www.zbmath.org/1475.780022022-01-14T13:23:02.489162ZPublisher's description: Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field.
Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing.
\begin{itemize}
\item Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides.
\item Part II explores solutions to paraxial, linear, and nonlinear wave equations.
\item Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics.
\item Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics.
\item Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers.
\item Part VI introduces super-resolution imaging and differential geometric methods in image processing.
\end{itemize}
As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica code in their appendices. The software codes and notebooks as well as color versions of the book's figures are available at \url {www.crcpress.com}.
The articles of this volume will be reviewed individually.
Indexed articles:
\textit{Padgett, Miles}, Orbital angular momentum: a ray optical interpretation, 3-12 [Zbl 1288.78028]
\textit{Alieva, Tatiana; Cámara, Alejandro; Bastiaans, Martin J.}, Wigner distribution moments for beam characterization, 13-51 [Zbl 1288.78026]
\textit{Calvo, Maria L.; Pérez-Ríos, Jesús; Lakshminarayanan, Vasudevan}, Dynamic programming applications in optics, 53-94 [Zbl 1288.78039]
\textit{Alonso, Miguel A.; Moore, Nicole J.}, Basis expansions for monochromatic field propagation in free space, 97-141 [Zbl 1288.78010]
\textit{Abramochkin, Eugeny; Alieva, Tatiana; Rodrigo, José A.}, Solutions of paraxial equations and families of Gaussian beams, 143-192 [Zbl 1288.78009]
\textit{Lakshminarayanan, Vasudevan; Nandy, Sudipta; Sridhar, Raghavendra}, The decomposition method to solve differential equations: optical applications, 193-232 [Zbl 1288.78012]
\textit{Kadic, Muamer; Guenneau, Sébastien; Enoch, Stefan}, An introduction to mathematics of transformational plasmonics, 235-277 [Zbl 1288.78019]
\textit{Sukharev, Maxim}, Plasmonics: computational approach, 279-299 [Zbl 1288.78029]
\textit{Başkai, Sibel; Kim, Y. S.}, Lorentz group in ray and polarization optics, 303-340 [Zbl 1288.78027]
\textit{Torre, Amalia}, Paraxial wave equation: Lie-algebra-based approach, 341-417 [Zbl 1288.78014]
\textit{Viana, Marlos}, Dihedral polynomials, 419-437 [Zbl 1288.78004]
\textit{Ban, Masashi}, Lie algebra and Liouville-space methods in quantum optics, 439-479 [Zbl 1290.81048]
\textit{Luis, Alfredo}, From classical to quantum light and vice versa: quantum phase-space methods, 483-506 [Zbl 1290.81227]
\textit{Zahid, Imrana Ashraf; Lakshminarayanan, Vasudevan}, Coherence functions in classical and quantum optics, 507-531 [Zbl 1288.78006]
\textit{Rybár, Tomáš; Ziman, Mário; Bužek, Vladimír}, Quantum memory channels in quantum optics, 533-552 [Zbl 1290.81020]
\textit{Simpkins, Jonathan D.; Stevenson, Robert L.}, An introduction to super-resolution imaging, 555-580 [Zbl 1298.94015]
\textit{ter Haar Romeny, Bart M.}, The differential structure of images, 581-597 [Zbl 1294.94007]Kompaneets equation for neutrinos: application to neutrino heating in supernova explosionshttps://www.zbmath.org/1475.800052022-01-14T13:23:02.489162Z"Suwa, Yudai"https://www.zbmath.org/authors/?q=ai:suwa.yudai"Tahara, Hiroaki W. H."https://www.zbmath.org/authors/?q=ai:tahara.hiroaki-w-h"Komatsu, Eiichiro"https://www.zbmath.org/authors/?q=ai:komatsu.eiichiroSummary: We derive a ``Kompaneets equation'' for neutrinos, which describes how the distribution function of neutrinos interacting with matter deviates from a Fermi-Dirac distribution with zero chemical potential. To this end, we expand the collision integral in the Boltzmann equation of neutrinos up to the second order in energy transfer between matter and neutrinos. The distortion of the neutrino distribution function changes the rate at which neutrinos heat matter, as the rate is proportional to the mean square energy of neutrinos, \(E_\nu^2\). For electron-type neutrinos the enhancement in \(E_\nu^2\) over its thermal value is given approximately by \(E_\nu^2/E_{\nu,\mathrm{thermal}}^2=1+0.086(V/0.1)^2\), where \(V\) is the bulk velocity of nucleons, while for the other neutrino species the enhancement is \((1+\delta_v)^3\); where \(\delta_v=mV^2/3k_{\mathrm{B}}T\) is the kinetic energy of nucleons divided by the thermal energy. This enhancement has a significant implication for supernova explosions, as it would aid neutrino-driven explosions.Quantum mechanicshttps://www.zbmath.org/1475.810012022-01-14T13:23:02.489162Z"Berera, Arjun"https://www.zbmath.org/authors/?q=ai:berera.arjun"Del Debbio, Luigi"https://www.zbmath.org/authors/?q=ai:del-debbio.luigiPublisher's description: Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.The planetary atom. A fictional account of George Adolphus Schott the forgotten physicist. With a foreword by Roald Hoffmann. Translated from the Frenchhttps://www.zbmath.org/1475.810022022-01-14T13:23:02.489162Z"Jean-Patrick Connerade, Chaunes"https://www.zbmath.org/authors/?q=ai:jean-patrick-connerade.chaunesPublisher's description: This largely imaginary biography recreates the life and times of George Adolphus Schott, a contemporary of Rutherford and Bohr, who criticized the Planetary Atom which was proposed to account for celebrated observations by Rutherford. Schott proved the Planetary Atom to be incompatible with fundamental properties of physics. Unfortunately, his work was cast aside because of Bohr's success in accounting for the structure of the atom. Later, it was found that Schott had, in fact, predicted important effects. Nonetheless, his contribution was forgotten and his discovery of Synchrotron Radiation was attributed to another.
In The Planetary Atom, Schott's interactions with eminent scientists of the time are reconstructed. The novel rehabilitates an unjustly forgotten British researcher and restores him to his rightful place as one of the great scientists of his time.Kurt Gödels notes on quantum mechanics. Transcriptions and commentshttps://www.zbmath.org/1475.810032022-01-14T13:23:02.489162ZPublisher's description: Kurt Gödel (1906--1978) -- eines der größten mathematischen Genies des 20. Jahrhunderts -- hat unter anderem ein umfangreiches Erbe aus Notizen und Arbeitsbüchern hinterlassen. Dieser Band enthält die bisher unveröffentlichten Arbeitsbücher zur Quantenmechanik aus den Jahren 1935/36. Von Tim Lethen aus der Gabelsberger Kurzschrift übertragen und von Oliver Passon kommentiert, dokumentiert diese Quelle die bisher vollkommen unbekannte, aber intensive Beschäftigung Gödels mit der Quantenmechanik und ihren philosophischen Implikationen. Damit handelt es sich um einen bedeutenden Beitrag zur Forschung über diesen vielseitigen Wissenschaftler, der auch wichtige Impulse zur Geschichte und Philosophie der Quantentheorie liefert.Anti-differentiation and the calculation of Feynman amplitudes. Selected papers based on the presentations at the conference, Zeuthen, Germany, October 2020https://www.zbmath.org/1475.810042022-01-14T13:23:02.489162ZPublisher's description: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
The articles of this volume will be reviewed individually.
Indexed articles:
\textit{Blümlein, Johannes}, Analytic integration methods in quantum field theory: an introduction, 1-33 [Zbl 07458360]
\textit{Ablinger, Jakob}, Extensions of the AZ-algorithm and the package multiintegrate, 35-61 [Zbl 07458361]
\textit{Acres, Kevin; Broadhurst, David}, Empirical determinations of Feynman integrals using integer relation algorithms, 63-82 [Zbl 07458362]
\textit{Bartels, Jochen}, N = 4 SYM gauge theories: the \(2 \rightarrow 6\) amplitude in the Regge limit, 83-106 [Zbl 07458363]
\textit{Bourjaily, Jacob L.; He, Yang-Hui; McLeod, Andrew J.; Spradlin, Marcus; Vergu, Cristian; Volk, Matthias; von Hippel, Matt; Wilhelm, Matthias}, Direct integration for multi-leg amplitudes: tips, tricks, and when they fail, 107-123 [Zbl 07458364]
\textit{Broedel, Johannes; Kaderli, André}, A geometrical framework for amplitude recursions: bridging between trees and loops, 125-144 [Zbl 07458365]
\textit{Dreyfus, Thomas; Weil, Jacques-Arthur}, Differential Galois theory and integration, 145-171 [Zbl 07458366]
\textit{Frellesvig, Hjalte}, Top-down decomposition: a cut-based approach to integral reductions, 173-188 [Zbl 07458367]
\textit{Kalmykov, Mikhail; Bytev, Vladimir; Kniehl, Bernd A.; Moch, Sven-Olaf; Ward, Bennie F. L.; Yost, Scott A.}, Hypergeometric functions and Feynman diagrams, 189-234 [Zbl 07458368]
\textit{Kotikov, Anatoly V.}, Differential equations and Feynman integrals, 235-259 [Zbl 07458369]
\textit{Koutschan, Christoph}, Holonomic anti-differentiation and Feynman amplitudes, 261-277 [Zbl 07458370]
\textit{Kreimer, Dirk}, Outer space as a combinatorial backbone for Cutkosky rules and coactions, 279-312 [Zbl 07458371]
\textit{Marquard, Peter}, Integration-by-parts: a survey, 313-320 [Zbl 07458372]
\textit{Moch, Sven-Olaf; Magerya, Vitaly}, Calculating four-loop corrections in QCD, 321-334 [Zbl 07458373]
\textit{Paule, Peter}, Contiguous relations and creative telescoping, 335-394 [Zbl 07458374]
\textit{Raab, Clemens G.}, Nested integrals and rationalizing transformations, 395-422 [Zbl 07458375]
\textit{Schneider, Carsten}, Term algebras, canonical representations and difference ring theory for symbolic summation, 423-485 [Zbl 07458376]
\textit{Smirnov, Vladimir A.}, Expansion by regions: an overview, 487-499 [Zbl 07458377]
\textit{Vermaseren, J. A. M.}, Some steps towards improving IBP calculations and related topics, 501-518 [Zbl 07458378]
\textit{Weinzierl, Stefan}, Iterated integrals related to Feynman integrals associated to elliptic curves, 519-545 [Zbl 07458379]Quantum arrangements. Contributions in honor of Michael Hornehttps://www.zbmath.org/1475.810052022-01-14T13:23:02.489162ZPublisher's description: This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. This collection includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony.
The articles of this volume will not be indexed individually.Ludwig Faddeev memorial. From hadrons to atoms: exploring the world of few-body systemshttps://www.zbmath.org/1475.810062022-01-14T13:23:02.489162ZPublisher's description: This issue is dedicated to the memorial of professor Ludwig Faddeev, who strongly influenced the physics of few-body systems mainly due to his theoretical works in what at present days are called the Faddeev equations, largely used by the few-body community to describe the dynamics and structure of few-body systems.
This issue contains the two winners of the 2018 Faddeev Medal, which was created to recognize distinguished achievements in Few-Body Physics. It is awarded every three years to a scientist who advanced the field of few-body physics significantly. In 2018 an international panel selected the winners of the 2018 award: Prof. Vitaly Efimov and Prof. Rudolf Grimm.
The contents show the deep influence of Prof. Faddeev in different fields of physics. The solutions of the Faddeev equations represented a challenge for many years and at present times from their solution theoretical models can be tested with great detail to experimental data. This has boosted the studied of few-nucleon systems and new methods have been developed as well.
Many contributions discuss different aspects of the few-nucleon problem from a theoretical and an experimental point of view. They represent the best of our knowledge at present times.Topos quantum theory with short posetshttps://www.zbmath.org/1475.810072022-01-14T13:23:02.489162Z"Harding, John"https://www.zbmath.org/authors/?q=ai:harding.john"Heunen, Chris"https://www.zbmath.org/authors/?q=ai:heunen.chrisSummary: Topos quantum mechanics, developed in [\textit{A. Döring}, ``Quantum states and measures on the spectral presheaf'', Adv. Sci. Lett. 2, No. 2, 291--301 (2009; \url{doi:10.1166/asl.2009.1037}); with \textit{J. Harding}, Houston J. Math. 42, No. 2, 559--568 (2016; Zbl 1360.46052); with \textit{C. Isham}, Lect. Notes Phys. 813, 753--937 (2011; Zbl 1253.81011); \textit{C. Flori}, A first course in topos quantum theory. Berlin: Springer (2013; Zbl 1280.81001); A second course in topos quantum theory. Cham: Springer (2018; Zbl 1398.81002); \textit{C. J. Isham} and \textit{J. Butterfield}, Int. J. Theor. Phys. 37, No. 11, 2669--2733 (1998; Zbl 0979.81018); ibid. 38, No. 3, 827--859 (1999; Zbl 1007.81009); ibid. 41, No. 4, 613--639 (2002; Zbl 1021.81002); \textit{J. Hamilton} et al., ibid. 39, No. 6, 1413--1436 (2000; Zbl 1055.81004)], creates a topos of presheaves over the poset \(\mathcal{V}(\mathcal{N})\) of abelian von Neumann subalgebras of the von Neumann algebra \(\mathcal{N}\) of bounded operators associated to a physical system, and established several results, including: (a) a connection between the Kochen-Specker theorem and the non-existence of a global section of the spectral presheaf; (b) a version of the spectral theorem for self-adjoint operators; (c) a connection between states of \(\mathcal{N}\) and measures on the spectral presheaf; and (d) a model of dynamics in terms of \(\mathcal{V}(\mathcal{N})\). We consider a modification to this approach using not the whole of the poset \(\mathcal{V}(\mathcal{N})\), but only its elements \(\mathcal{V}(\mathcal{N})^*\) of height at most two. This produces a different topos with different internal logic. However, the core results (a)-(d) established using the full poset \(\mathcal{V}(\mathcal{N})\) are also established for the topos over the smaller poset, and some aspects simplify considerably. Additionally, this smaller poset has appealing aspects reminiscent of projective geometry.Stochasticity and Bell-type quantum field theoryhttps://www.zbmath.org/1475.810082022-01-14T13:23:02.489162Z"Oldofredi, Andrea"https://www.zbmath.org/authors/?q=ai:oldofredi.andreaSummary: This paper critically discusses an objection proposed by Nikolić against the naturalness of the stochastic dynamics implemented by the Bell-type quantum field theory, an extension of Bohmian mechanics able to describe the phenomena of particles creation and annihilation. Here I present: (1) Nikolić's ideas for a pilot-wave theory accounting for QFT phenomenology evaluating the robustness of his criticism, (2) Bell's original proposal for a Bohmian QFT with a particle ontology and (3) the mentioned Bell-type QFT. I will argue that although Bell's model should be interpreted as a heuristic example showing the possibility to extend Bohm's pilot-wave theory to the domain of QFT, the same judgement does not hold for the Bell-type QFT, which is candidate to be a promising possible alternative proposal to the standard version of quantum field theory. Finally, \textit{contra} Nikolić, I will provide arguments in order to show how a stochastic dynamics is perfectly compatible with a Bohmian quantum theory.Positivity and nonadditivity of quantum capacities using generalized erasure channelshttps://www.zbmath.org/1475.810092022-01-14T13:23:02.489162Z"Siddhu, Vikesh"https://www.zbmath.org/authors/?q=ai:siddhu.vikesh"Griffiths, Robert B."https://www.zbmath.org/authors/?q=ai:griffiths.robert-bEditorial remark: No review copy delivered.Pursuing the fundamental limits for quantum communicationhttps://www.zbmath.org/1475.810102022-01-14T13:23:02.489162Z"Wang, Xin"https://www.zbmath.org/authors/?q=ai:wang.xin.7|wang.xin.9|wang.xin.6|wang.xin.11|wang.xin.4|wang.xin.10|wang.xin.1|wang.xin.8|wang.xin|wang.xin.2|wang.xin.5|wang.xin.12|wang.xin.3|wang.xin.13Editorial remark: No review copy delivered.When is the Chernoff exponent for quantum operations finite?https://www.zbmath.org/1475.810112022-01-14T13:23:02.489162Z"Yu, Nengkun"https://www.zbmath.org/authors/?q=ai:yu.nengkun"Zhou, Li"https://www.zbmath.org/authors/?q=ai:zhou.liEditorial remark: No review copy delivered.Finite block length analysis on quantum coherence distillation and incoherent randomness extractionhttps://www.zbmath.org/1475.810122022-01-14T13:23:02.489162Z"Hayashi, Masahito"https://www.zbmath.org/authors/?q=ai:hayashi.masahito"Fang, Kun"https://www.zbmath.org/authors/?q=ai:fang.kun"Wang, Kun"https://www.zbmath.org/authors/?q=ai:wang.kunEditorial remark: No review copy delivered.Single-shot secure quantum network coding for general multiple unicast network with free one-way public communicationhttps://www.zbmath.org/1475.810132022-01-14T13:23:02.489162Z"Kato, Go"https://www.zbmath.org/authors/?q=ai:kato.go"Owari, Masaki"https://www.zbmath.org/authors/?q=ai:owari.masaki"Hayashi, Masahito"https://www.zbmath.org/authors/?q=ai:hayashi.masahitoEditorial remark: No review copy delivered.Algebraic construction of spherical harmonicshttps://www.zbmath.org/1475.810142022-01-14T13:23:02.489162Z"Ogawa, Naohisa"https://www.zbmath.org/authors/?q=ai:ogawa.naohisaSummary: The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the \(SU(2)\) algebra and its eigenvalue \(l(l + 1)\hbar^2\), where l is non-negative integer, is easily obtained by an algebraic method. Therefore the shape of the wave function may also be obtained by extending the algebraic method. In this paper, we describe the method and show that wave functions with different quantum numbers are connected by a rotational group in the cases of \(l = 0, 1\) and 2.Killing spinors from classical \(r\)-matriceshttps://www.zbmath.org/1475.810152022-01-14T13:23:02.489162Z"Orlando, Domenico"https://www.zbmath.org/authors/?q=ai:orlando.domenico"Reffert, Susanne"https://www.zbmath.org/authors/?q=ai:reffert.susanne"Sekiguchi, Yuta"https://www.zbmath.org/authors/?q=ai:sekiguchi.yuta"Yoshida, Kentaroh"https://www.zbmath.org/authors/?q=ai:yoshida.kentarohMotivating dualitieshttps://www.zbmath.org/1475.810162022-01-14T13:23:02.489162Z"Read, James"https://www.zbmath.org/authors/?q=ai:read.james"Møller-Nielsen, Thomas"https://www.zbmath.org/authors/?q=ai:moller-nielsen.thomasSummary: There exists a common view that for theories related by a `duality', dual models typically may be taken ab initio to represent the same physical state of affairs, i.e. to correspond to the same possible world. We question this view, by drawing a parallel with the distinction between `interpretational' and `motivational' approaches to symmetries.Fluctuations and non-equilibrium phenomena in strongly-correlated ultracold atomshttps://www.zbmath.org/1475.820012022-01-14T13:23:02.489162Z"Nagao, Kazuma"https://www.zbmath.org/authors/?q=ai:nagao.kazumaThis work is devoted to the study of fluctuation effects on non-equilibrium quantum many-body phenomena in ultra-cold atoms trapped by an optical-lattice. The results are achieved through a theoretical analysis of near-and-far-from equilibrium dynamics in addition to relevant numerical simulations which agree with the theoretical analysis.
In the first part of the work, the stability and visibility of the Higgs mode in ultra-cold-gas systems is examined while in the second part, investigations on far-from-equilibrium quantum-quench dynamics of Bose gases in higher-dimensional optical lattices are carried out. By adopting a semi-classical approximation formulated by a phase-space representation of quantum systems, a quantitative simulation of the energy-redistribution is presented. The approximation approach used herein is the truncated Wigner approximation (TWA), which systematically provides a leading-order correction of the fluctuations to the mean-field or saddle-point dynamics. Finally, numerical simulations are employed in the redistribution dynamics of the kinetic and interaction energies in a 3D system beginning from the opposite limit after a generalization of the TWA is made. It is then observed that the results from the numerical simulation of the TWA agrees well with the experimental data with no fitting parameter.
Chapter 2 includes literature on ultra-cold Bose gases trapped by optical-lattice potentials. After deriving a single-band Bose Hubbard model within the tight-binding approximation, a summary of the ground state properties of the Bose-Hubbard model with focus on the superfluid mott insulator quantum phase transitions is presented. To present adequate points of discussion about the collective excitations of strongly correlated superfluid near transitions, standing wave lasers far detuned from atomic resonance are used to generate optical lattices. In addition, a brief review of the Bose-Hubbard models are presented. Next, the superfluid-mott-insulator quantum phase transitions involving discussion of the mean-field theory of the superfluid mott insulator transition and the field theoretical description for the quantum phase transition is presented. Using real-time dynamics of the commensurate superfluid near the mott insulator transition, more literature is presented on the Higgs and Nambu-Goldstone modes. The final work done in this chapter involves a description of the Hilbert-space truncation and effective pseudospin-1 models which focuses on the strongly interacting regime of the Bose-Hubbard model for $U/J >>1$.
Chapter 3 explores a phase-space method for expressing quantum systems by means of c-number functions defined in a phase space with special focus placed on the coherent-state Wigner representation of Bose fields. The main remarkable part of this chapter is the formulation of the dynamics of a system of Bose fields in terms of the phase-space representation. These systems after being isolated from external environments results in a peculiar observation that the real-time dynamics of the Bose fields are governed by the von-Neumann equation.
Chapter 4 presents the responses of the Higgs modes to the temporal modulations of the lattice amplitude as well as onsite interaction strength in the cubic optical lattice. While analyzing the linear response functions for the effective pseudospin-1 model, using the perturbative calculation of the finite-temperature Green's function, a review is presented on the linear response theory for external modulations where the kinetic energy modulations are explored in addition to onsite-interaction energy modulations. A description of the interactions between collective modes and linear response analysis is also presented. The results from the numerical simulation in this chapter show that the Higgs-mode resonance can survive as a sharp peak in the dynamical susceptibility even at typical temperatures of experiments until $T = 2J$.
Chapter 5 investigates far-from-equilibrium dynamics of Bose gases in optical lattices after sudden quantum quenches from a Mott insulating state in a 3D optical lattice, by using the TWA to numerically simulate the redistribution dynamics of both the kinetic and onsite-interaction energies. Further explorations are carried out regarding the correlation propagation over a two-dimensional lattice. Results from the simulations suggest that when the system is initially prepared in a coherent product state, the mean propagation velocity of the wave packet in the correlation function clearly depends on the final interaction strength of the quench. Thus, with these results it is possible to conclude that the numerical simulation from the TWA agrees well with the experimental data without any fitting parameter.
In conclusion, several theoretical analyses of non-equilibrium quantum many-body problems have been explored. Experimental works using approaches that consider effects of fluctuations beyond the mean-field treatments have been the trigger for the simulations leading to the main results. This work focuses on near- and far-from-equilibrium dynamics of ultra-cold Bose atoms in optical lattices; it offers an important step towards deeper understanding of quantum many-body phenomena realized from real experiments involving ultra-cold atoms.
Reviewer: Maria C. Mariani (El Paso)The development of renormalization group methods for particle physics: formal analogies between classical statistical mechanics and quantum field theoryhttps://www.zbmath.org/1475.820082022-01-14T13:23:02.489162Z"Fraser, Doreen"https://www.zbmath.org/authors/?q=ai:fraser.doreenSummary: Analogies between classical statistical mechanics and quantum field theory (QFT) played a pivotal role in the development of renormalization group (RG) methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's [\textit{K Wilson}, ``The renormalization group and the \(\varepsilon\) expansion'', Phys. Rep. 12, No. 2, 75--199 (1974; \url{doi:10.1016/0370-1573(74)90023-4})]. The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics.Localization and IDS regularity in the disordered Hubbard model within Hartree-Fock theoryhttps://www.zbmath.org/1475.820112022-01-14T13:23:02.489162Z"Matos, Rodrigo"https://www.zbmath.org/authors/?q=ai:matos.rodrigo"Schenker, Jeffrey"https://www.zbmath.org/authors/?q=ai:schenker.jeffrey-hSummary: Using the fractional moment method it is shown that, within the Hartree-Fock approximation for the disordered Hubbard Hamiltonian, weakly interacting Fermions at positive temperature exhibit localization, suitably defined as exponential decay of eigenfunction correlators. Our result holds in any dimension in the regime of large disorder and at any disorder in the one dimensional case. As a consequence of our methods, we are able to show Hölder continuity of the integrated density of states with respect to energy, disorder and interaction.Solution to the quantum symmetric simple exclusion process: the continuous casehttps://www.zbmath.org/1475.820142022-01-14T13:23:02.489162Z"Bernard, Denis"https://www.zbmath.org/authors/?q=ai:bernard.denis"Jin, Tony"https://www.zbmath.org/authors/?q=ai:jin.tonySummary: The quantum symmetric simple exclusion process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.Stationary quantum BGK model for bosons and fermions in a bounded intervalhttps://www.zbmath.org/1475.820182022-01-14T13:23:02.489162Z"Bae, Gi-Chan"https://www.zbmath.org/authors/?q=ai:bae.gi-chan"Yun, Seok-Bae"https://www.zbmath.org/authors/?q=ai:yun.seok-baeIn this work, the authors consider the existence problem for stationary relaxational models of the quantum Boltzmann equation. The existence of mild solution to the fermionic or bosonic quantum BGK model with inflow boundary data is proved. The physical motivation of the problem is the situation in which there is a gas flow between two parallel gas-emitting plates of infinite size. There have not been many results on the analysis of such quantum BGK models. The paper is therefore quite interesting. The proof is based on a contraction mapping argument. The authors also show that the transition from the non-condensed state to the condensated state, or from the non-saturated state to the saturated state does not arise.
Reviewer: Minh-Binh Tran (Dallas)Electrons on mesoscopic length scales: the role of the electron phasehttps://www.zbmath.org/1475.820192022-01-14T13:23:02.489162Z"Stampfer, Christoph"https://www.zbmath.org/authors/?q=ai:stampfer.christophFrom the text: The first chapter of this book deals with mesoscopic physics, a field which describesthe properties of electrons at length scales, where the phase of the electron wave function is crucial for the observed properties. Generally, electrons in metals and semiconductors experience an irregular latticepotential. It arises from defects, lattice imperfections, grain boundaries, vacancies,doped impurities as well as from thermally induced lattice vibrations (phonons).
For the entire collection see [Zbl 1414.82005].Special relativity and classical field theory. The theoretical minimum: everything you need to know to start with physics. Translated from the English by André Cabannes and Benoît Clenethttps://www.zbmath.org/1475.830012022-01-14T13:23:02.489162Z"Susskind, Léonard"https://www.zbmath.org/authors/?q=ai:susskind.leonard"Friedman, Art"https://www.zbmath.org/authors/?q=ai:friedman.artPublisher's description: Le physicien Leonard Susskind et l'ingénieur en informatique Art Friedman sont de retour. Après nous avoir fait découvrir la mécanique classique et la mécanique quantique dans les deux premiers volumes de cette série mondialement acclamée (Le Minimum Théorique), Leonard Susskind et Art Friedman s'attachent ici à la théorie des champs, qui sous-tend la gravitation de Newton, l'électromagnétisme de Maxwell et la relativité restreinte d'Einstein. Sur la base d'équations mathématiques aussi simples que possibles (mais pas plus) et de leurs sympathiques alter egos Art et Lenny qui introduisent chaque leçon par un petit dialogue humoristique, Susskind et Friedman nous emmènent à la découverte des ondes, des forces et des particules, au travers d'un monde gouverné par les lois de la relativité restreinte. Ce troisième volume ne se départit pas de la marque qui a fait le succès des deux précédents: un contenu à la fois accessible et rigoureux, et indispensable à quiconque désireux d'aller au-delà de la simple vulgarisation sans savoir par où commencer.
See also the review of the English original in Zbl 1383.83002.Causal fermion systems and the ETH approach to quantum theoryhttps://www.zbmath.org/1475.830032022-01-14T13:23:02.489162Z"Finster, Felix"https://www.zbmath.org/authors/?q=ai:finster.felix"Fröhlich, Jürg"https://www.zbmath.org/authors/?q=ai:frohlich.jurg-martin"Oppio, Marco"https://www.zbmath.org/authors/?q=ai:oppio.marco"Paganini, Claudio F."https://www.zbmath.org/authors/?q=ai:paganini.claudio-fSummary: After reviewing the theory of ``causal fermion systems'' (CFS theory) and the ``Events, Trees, and Histories Approach'' to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of ``events'', as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length.Light propagation in 2PN approximation in the field of one moving monopole. II: Boundary value problemhttps://www.zbmath.org/1475.830112022-01-14T13:23:02.489162Z"Zschocke, Sven"https://www.zbmath.org/authors/?q=ai:zschocke.svenNoncommutative geometry of the quantum clockhttps://www.zbmath.org/1475.830132022-01-14T13:23:02.489162Z"Mignemi, S."https://www.zbmath.org/authors/?q=ai:mignemi.salvatore"Uras, N."https://www.zbmath.org/authors/?q=ai:uras.nSummary: We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.Scalar gravitational radiation from binaries: Vainshtein mechanism in time-dependent systemshttps://www.zbmath.org/1475.830222022-01-14T13:23:02.489162Z"Dar, Furqan"https://www.zbmath.org/authors/?q=ai:dar.furqan"de Rham, Claudia"https://www.zbmath.org/authors/?q=ai:de-rham.claudia"Deskins, J. Tate"https://www.zbmath.org/authors/?q=ai:deskins.j-tate"Giblin, John T. Jr"https://www.zbmath.org/authors/?q=ai:giblin.john-t-jr"Tolley, Andrew J."https://www.zbmath.org/authors/?q=ai:tolley.andrew-jQuasinormal modes of bumblebee wormholehttps://www.zbmath.org/1475.830252022-01-14T13:23:02.489162Z"Oliveira, R."https://www.zbmath.org/authors/?q=ai:oliveira.r-r-s"Dantas, D. M."https://www.zbmath.org/authors/?q=ai:dantas.d-m"Santos, Victor"https://www.zbmath.org/authors/?q=ai:santos.victor"Almeida, C. A. S."https://www.zbmath.org/authors/?q=ai:almeida.carlos-a-sEmergence of time in loop quantum gravityhttps://www.zbmath.org/1475.830282022-01-14T13:23:02.489162Z"Brahma, Suddhasattwa"https://www.zbmath.org/authors/?q=ai:brahma.suddhasattwaSummary: Loop quantum gravity has formalized a robust scheme in resolving classical singularities in a variety of symmetry-reduced models of gravity. In this essay, we demonstrate that the same quantum correction that is crucial for singularity resolution is also responsible for the phenomenon of signature change in these models, whereby one effectively transitions from a ``fuzzy'' Euclidean space to a Lorentzian space-time in deep quantum regimes. As long as one uses a quantization scheme that respects covariance, holonomy corrections from loop quantum gravity generically leads to nonsingular signature change, thereby giving an emergent notion of time in the theory. Robustness of this mechanism is established by comparison across a large class of midisuperspace models and allowing for diverse quantization ambiguities. Conceptual and mathematical consequences of such an underlying quantum-deformed spacetime are briefly discussed.
For the entire collection see [Zbl 1460.81001].Tabletop experiments for quantum gravity: a user's manualhttps://www.zbmath.org/1475.830292022-01-14T13:23:02.489162Z"Carney, Daniel"https://www.zbmath.org/authors/?q=ai:carney.daniel"Stamp, Philip C. E."https://www.zbmath.org/authors/?q=ai:stamp.philip-c-e"Taylor, Jacob M."https://www.zbmath.org/authors/?q=ai:taylor.jacob-mTowards a swampland global symmetry conjecture using weak gravityhttps://www.zbmath.org/1475.830302022-01-14T13:23:02.489162Z"Daus, Tristan"https://www.zbmath.org/authors/?q=ai:daus.tristan"Hebecker, Arthur"https://www.zbmath.org/authors/?q=ai:hebecker.arthur"Leonhardt, Sascha"https://www.zbmath.org/authors/?q=ai:leonhardt.sascha"March-Russell, John"https://www.zbmath.org/authors/?q=ai:march-russell.johnSummary: It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be \textit{quantitatively} constrained by quantum gravity or swampland arguments. We provide such a bound for an important class of global symmetries: Those arising from a gauged \(U(1)\) with the vector made massive via Higgsing with an axion. The latter necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory. As a result, instanton-induced symmetry breaking operators with a suppression factor not smaller than \(\exp(- M_{\mathrm{P}}^2/\Lambda^2)\) are present, where \(\Lambda\) is a cutoff of the 4d effective theory. We provide a general argument and clarify the meaning of \(\Lambda \). Simple 4d and 5d models are presented to illustrate this, and we recall that this is the standard way in which things work out in string compactifications with brane instantons. The relation of our constraint to bounds that can be derived from wormholes or gravitational instantons and to those motivated by black-hole effects at finite temperature are discussed, and we present a generalization of the Giddings-Strominger wormhole solution to the case of a gauge-derived \(U(1)\) global symmetry. Finally, we discuss potential loopholes to our arguments.Chronic incompleteness, final theory claims, and the lack of free parameters in string theoryhttps://www.zbmath.org/1475.830312022-01-14T13:23:02.489162Z"Dawid, Richard"https://www.zbmath.org/authors/?q=ai:dawid.richardSummary: Three central questions that face a future philosophy of quantum gravity: Does quantum gravity eliminate spacetime as fundamental structure? How does quantum gravity explain the appearance of spacetime? What are the broader implications of quantum gravity for metaphysical (and other) accounts of the world? In this essay I begin to lay out a conceptual scheme for (1) analyzing dualities as cases of theoretical equivalence and (2) assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about (3) the nature of spacetime in quantum gravity and (4) broader philosophical and physical discussions of spacetime. I apply this scheme to questions (3) and (4) for gauge/gravity dualities. I argue that the things that are physically relevant are those that stand in a bijective correspondence under duality: the common core of the two models. I therefore conclude that most of the mathematical and physical structures that we are familiar with, in these models (the dimension of spacetime, tensor fields, Lie groups), are largely, though crucially never entirely, not part of that common core. Thus, the interpretation of dualities for theories of quantum gravity compels us to rethink the roles that spacetime, and many other tools in theoretical physics, play in theories of spacetime.
For the entire collection see [Zbl 1460.81001].Back to Parmenideshttps://www.zbmath.org/1475.830352022-01-14T13:23:02.489162Z"Gomes, Henrique"https://www.zbmath.org/authors/?q=ai:gomes.henrique-de-aSummary: After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns a quantization of the principle of relative simultaneity. This leads me to a distinction between time and space, to a further degree than that present in the canonical approach to general relativity. With this distinction, one can make sense of superpositions as interference between alternative paths in the relational configuration space of the entire universe. But the full use of relationalism brings us to a timeless picture of nature, as it does in the canonical approach (which culminates in the Wheeler-DeWitt equation). After a discussion of Parmenides and the Eleatics's rejection of time, I show that there is middle ground between their view of absolute timelessness and a view of physics taking place in timeless configuration space. In this middle ground, even though change does not fundamentally exist, the illusion of change can be recovered in a way not permitted by Parmenides. It is recovered through a particular density distribution over configuration space that gives rise to records. Incidentally, this distribution seems to have the potential to dissolve further aspects of the measurement problem that can still be argued to haunt the application of decoherence to many-worlds quantum mechanics. I end with a discussion indicating that the conflict between the conclusions of this paper and our view of the continuity of the self may still intuitively bother us. Nonetheless, those conclusions should be no more challenging to our intuition than Derek Parfit's thought experiments on the subject.
For the entire collection see [Zbl 1460.81001].The Bronstein hypercube of quantum gravityhttps://www.zbmath.org/1475.830362022-01-14T13:23:02.489162Z"Oriti, Daniele"https://www.zbmath.org/authors/?q=ai:oriti.danieleSummary: We argue for enlarging the traditional view of quantum gravity, based on `quantizing GR', to include explicitly the nonspatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and some semiclassical arguments) and to focus more on the issue of the emergence of continuum spacetime and geometry from their collective dynamics. We also discuss some recent developments in quantum gravity research, aiming at realizing these ideas, in the context of group field theory, random tensor models, simplicial quantum gravity, loop quantum gravity, and spin foam models.
For the entire collection see [Zbl 1460.81001].Non-perturbative unitarity and fictitious ghosts in quantum gravityhttps://www.zbmath.org/1475.830372022-01-14T13:23:02.489162Z"Platania, Alessia"https://www.zbmath.org/authors/?q=ai:platania.alessia-benedetta"Wetterich, Christof"https://www.zbmath.org/authors/?q=ai:wetterich.christofSummary: We discuss aspects of non-perturbative unitarity in quantum field theory. The additional ghost degrees of freedom arising in ``truncations'' of an effective action at a finite order in derivatives could be fictitious degrees of freedom. Their contributions to the fully-dressed propagator -- the residues of the corresponding ghost-like poles -- vanish once all operators compatible with the symmetry of the theory are included in the effective action. These ``fake ghosts'' do not indicate a violation of unitarity.Von Neumann stability of modified loop quantum cosmologieshttps://www.zbmath.org/1475.830392022-01-14T13:23:02.489162Z"Saini, Sahil"https://www.zbmath.org/authors/?q=ai:saini.sahil"Singh, Parampreet"https://www.zbmath.org/authors/?q=ai:singh.parampreetWhat can (mathematical) categories tell us about spacetime?https://www.zbmath.org/1475.830412022-01-14T13:23:02.489162Z"Sanders, Ko"https://www.zbmath.org/authors/?q=ai:sanders.koSummary: It is widely believed that in quantum theories of gravity, the classical description of spacetime as a manifold is no longer viable as a fundamental concept. Instead, spacetime emerges as an approximation in appropriate regimes. In order to understand what is required to explain this emergence, it is necessary to have a good understanding of the classical structure of spacetime. I focus on the concept of spacetime as it appears in locally covariant quantum field theory (LCQFT), an axiomatic framework for describing quantum field theories in the presence of gravitational background fields. A key aspect of LCQFT is the way in which it formulates locality and general covariance, using the language of category theory. I argue that the use of category theory gives a precise and explicit statement of how spacetime acts as an organizing principle in a certain systems view of the world. Along the way I indicate how physical theories give rise to categories that act as a kind of model for modal logic, and how the categorical view of spacetime shifts the emphasis away from the manifold structure. The latter point suggests that the view of spacetime as an organizing principle may persist, perhaps in a generalized way, even in a quantum theory of gravity. I mention some new questions, which this shift in emphasis raises.
For the entire collection see [Zbl 1460.81001].From Euclidean to Lorentzian loop quantum gravity via a positive complexifierhttps://www.zbmath.org/1475.830422022-01-14T13:23:02.489162Z"Varadarajan, Madhavan"https://www.zbmath.org/authors/?q=ai:varadarajan.madhavanExtending Lewisian modal metaphysics from a specific quantum gravity perspectivehttps://www.zbmath.org/1475.830432022-01-14T13:23:02.489162Z"Vistarini, Tiziana"https://www.zbmath.org/authors/?q=ai:vistarini.tizianaSummary: It is commonly held in many philosophy of quantum gravity circles that endorsing Lewis ontology of modal realism is incompatible with endorsing the fundamental physical ontology of any quantum gravity theory. The unsolvable tension would be between the Lewis metaphysical commitment to the fundamentality of space and time and the physical lesson of quantum gravity about the disappearance of space and time from the fundamental structure of the world. In this essay I argue against the idea that the tension is unsolvable. This analysis does not apply to quantum gravity in genera, but only to quantum string theory.
For the entire collection see [Zbl 1460.81001].On the symmetry of \(T \bar{T}\) deformed CFThttps://www.zbmath.org/1475.830442022-01-14T13:23:02.489162Z"He, Miao"https://www.zbmath.org/authors/?q=ai:he.miao"Gao, Yi-hong"https://www.zbmath.org/authors/?q=ai:gao.yihongSummary: We propose a symmetry of \(T \bar{T}\) deformed 2D CFT, which preserves the trace relation. The deformed conformal killing equation is obtained. Once we consider the background metric runs with the deformation parameter \(\mu \), the deformation contributes an additional term in conformal killing equation, which plays the role of renormalization group flow of metric. The conformal symmetry coincides with the fixed point. On the gravity side, this deformed conformal killing equation can be described by a new boundary condition of \(\mathrm{AdS}_3\). In addition, based on the deformed conformal killing equation, we derive that the stress tensor of the deformed CFT equals to Brown-York's quasilocal stress tensor on a finite boundary with a counterterm. For a specific example, BTZ black hole, we get \(T \bar{T}\) deformed conformal killing vectors and the associated conserved charges are also studied.Purely triplet seesaw and leptogenesis within cosmological bound, dark matter, and vacuum stabilityhttps://www.zbmath.org/1475.830462022-01-14T13:23:02.489162Z"Parida, Mina Ketan"https://www.zbmath.org/authors/?q=ai:parida.mina-ketan"Chakraborty, Mainak"https://www.zbmath.org/authors/?q=ai:chakraborty.mainak"Nanda, Swaraj Kumar"https://www.zbmath.org/authors/?q=ai:nanda.swaraj-kumar"Samantaray, Riyanka"https://www.zbmath.org/authors/?q=ai:samantaray.riyankaSummary: In a novel standard model extension it has been suggested that, even in the absence of right-handed neutrinos and type-I seesaw, purely triplet leptogenesis leading to baryon asymmetry of the universe can be realized by two heavy Higgs triplets which also provide type-II seesaw ansatz for neutrino masses. In this work we discuss this model predictions for hierarchical neutrino masses in concordance with recently determined cosmological bounds and oscillation data including \(\theta_{23}\) in the second octant and large Dirac CP phases. We find that for both normal and inverted orderings, the model fits the oscillation data with the sum of the three neutrino masses consistent with current cosmological bounds determined from Planck satellite data. In addition, using this model ansatz for CP-asymmetry and solutions of Boltzmann equations, we also show how successful predictions of baryon asymmetry emerges in the cases of both unflavoured and two-flavoured leptogeneses. With additional \(Z_2\) discrete symmetry, a minimal extension of this model is further shown to predict a scalar singlet WIMP dark matter in agreement with direct and indirect observations which also resolves the issue of vacuum instability persisting in the original model. Although the combined constraints due to relic density and direct detection cross section allow this scalar singlet dark matter mass to be \(m_\xi = 750\) GeV, the additional vacuum stability constraint pushes this limiting value to \(m_\xi = 1.3\) TeV which is verifiable by ongoing experiments. We also discuss constraint on the model parameters for the radiative stability of the standard Higgs mass.Signal from sterile neutrino dark matter in extra \(U(1)\) model at direct detection experimenthttps://www.zbmath.org/1475.830472022-01-14T13:23:02.489162Z"Seto, Osamu"https://www.zbmath.org/authors/?q=ai:seto.osamu"Shimomura, Takashi"https://www.zbmath.org/authors/?q=ai:shimomura.takashi.1Summary: We examine the possibility that direct dark matter detection experiments find decay products from sterile neutrino dark mater in \(U(1)_{B-L}\) and \(U (1)_R\) models. This is possible if the sterile neutrino interacts with a light gauge boson, and decays into a neutrino and the light gauge boson with a certain lifetime. This decay produces energetic neutrinos scattering off nuclei with a large enough recoil energy in direct dark matter detection experiments. We stress that direct dark matter detection experiments can explore not only WIMP but also sterile neutrino dark matter.Top partners tackling vector dark matterhttps://www.zbmath.org/1475.830482022-01-14T13:23:02.489162Z"Yepes, Juan"https://www.zbmath.org/authors/?q=ai:yepes.juanSummary: The WIMP-nucleon scattering cross section in a simple dark matter model and its constraints from the latest direct detection experiment are treated here at the loop level. We consider a scenario with an emerging vector dark matter field that interacts with the Standard Model quarks, via loop contributions that are sourced from a scalar mediator. The involved parameter space for the dark matter-mediator masses is constrained by the Xenon1T limit and the neutrino floor. The current direct detection bounds are eluded by invoking the top partners in a Composite Higgs model, whose scale mass helps us in suppressing the WIMP-nucleon cross section.Barrow black hole corrected-entropy model and Tsallis nonextensivityhttps://www.zbmath.org/1475.830502022-01-14T13:23:02.489162Z"Abreu, Everton M. C."https://www.zbmath.org/authors/?q=ai:abreu.everton-m-c"Ananias Neto, Jorge"https://www.zbmath.org/authors/?q=ai:neto.jorge-ananiasSummary: The quantum scenario concerning Hawking radiation, gives us a precious clue that a black hole has its temperature directly connected to its area gravity and that its entropy is proportional to the horizon area. These results have shown that there exist a deep association between thermodynamics and gravity. The recently introduced Barrow formulation of back holes entropy, influenced by the spacetime geometry, shows the quantum fluctuations effects through Barrow exponent, \(\Delta\), where \(\Delta = 0\) represents the usual spacetime and its maximum value, \(\Delta = 1\), characterizes a fractal spacetime. The quantum fluctuations are responsible for such fractality. Loop quantum gravity approach provided the logarithmic corrections to the entropy. This correction arises from quantum and thermal equilibrium fluctuations. In this paper we have analyzed the nonextensive thermodynamical effects of the quantum fluctuations upon the geometry of a Barrow black hole. We discussed the Tsallis' formulation of this logarithmically corrected Barrow entropy to construct the equipartition law. Besides, we obtained a master equation that provides the equipartition law for any value of the Tsallis \(q\)-parameter and we analyzed several different scenarios. After that, the heat capacity were calculated and the thermal stability analysis was carried out as a function of the main parameters, namely, one of the so-called pre-factors, \(q\) and \(\Delta\).Quantum-corrected scattering and absorption of a Schwarzschild black hole with GUPhttps://www.zbmath.org/1475.830512022-01-14T13:23:02.489162Z"Anacleto, M. A."https://www.zbmath.org/authors/?q=ai:anacleto.m-a"Brito, F. A."https://www.zbmath.org/authors/?q=ai:brito.fabrito-a"Campos, J. A. V."https://www.zbmath.org/authors/?q=ai:campos.jose-andre-v"Passos, E."https://www.zbmath.org/authors/?q=ai:passos.eduardoSummary: In this paper we have implemented quantum corrections for the Schwarzschild black hole metric using the generalized uncertainty principle (GUP) in order to investigate the scattering process. We mainly compute, at the low energy limit, the differential scattering and absorption cross section by using the partial wave method. We determine the phase shift analytically and verify that these quantities are modified by the GUP. We found that due to the quantum corrections from the GUP the absorption is not zero as the mass parameter goes to zero. A numerical analysis has also been performed for arbitrary frequencies.Resonant Hawking radiation as an instabilityhttps://www.zbmath.org/1475.830542022-01-14T13:23:02.489162Z"Bermudez, David"https://www.zbmath.org/authors/?q=ai:bermudez.david"Leonhardt, Ulf"https://www.zbmath.org/authors/?q=ai:leonhardt.ulfQuasinormal modes of Dirac spinors in the background of rotating black holes in four and five dimensionshttps://www.zbmath.org/1475.830552022-01-14T13:23:02.489162Z"Blázquez-Salcedo, Jose Luis"https://www.zbmath.org/authors/?q=ai:blazquez-salcedo.jose-luis"Knoll, Christian"https://www.zbmath.org/authors/?q=ai:knoll.christianTunnelling processes for Hadamard states through a 2+1 dimensional black hole and Hawking radiationhttps://www.zbmath.org/1475.830572022-01-14T13:23:02.489162Z"Bussola, Francesco"https://www.zbmath.org/authors/?q=ai:bussola.francesco"Dappiaggi, Claudio"https://www.zbmath.org/authors/?q=ai:dappiaggi.claudioCorotating dyonic binary black holeshttps://www.zbmath.org/1475.830582022-01-14T13:23:02.489162Z"Cabrera-Munguia, I."https://www.zbmath.org/authors/?q=ai:cabrera-munguia.iSummary: This paper is dedicated to derive and study binary systems of identical corotating dyonic black holes separated by a massless strut -- two 5-parametric corotating binary black hole models endowed with both electric and magnetic charges -- where the dyonic black holes carrying equal/opposite electromagnetic charges in the first/second model satisfy the extended Smarr formula for the mass including the magnetic charge as a fourth conserved parameter.Special geometry, Hessian structures and applicationshttps://www.zbmath.org/1475.830602022-01-14T13:23:02.489162Z"Cardoso, Gabriel Lopes"https://www.zbmath.org/authors/?q=ai:lopes-cardoso.gabriel"Mohaupt, Thomas"https://www.zbmath.org/authors/?q=ai:mohaupt.thomasSummary: The target space geometry of abelian vector multiplets in \(\mathcal{N} = 2\) theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometries of four- and five-dimensional vector multiplets. We formulate \(\mathcal{N} = 2\) theories in terms of Hessian structures and give various concrete applications of Hessian geometry, ranging from static BPS black holes in four and five space-time dimensions to topological string theory, emphasizing the role of the Hesse potential. We also discuss the r-map and c-map which relate the special geometries of vector multiplets to each other and to hypermultiplet geometries. By including time-like dimensional reductions, we obtain theories in Euclidean signature, where the scalar target spaces carry para-complex versions of special geometry.Quasi-normal modes and fermionic vacuum decay around a Kerr black holehttps://www.zbmath.org/1475.830612022-01-14T13:23:02.489162Z"Coutant, Antonin"https://www.zbmath.org/authors/?q=ai:coutant.antonin"Millington, Peter"https://www.zbmath.org/authors/?q=ai:millington.peterAnalytical correspondence between shadow radius and black hole quasinormal frequencieshttps://www.zbmath.org/1475.830622022-01-14T13:23:02.489162Z"Cuadros-Melgar, B."https://www.zbmath.org/authors/?q=ai:cuadros-melgar.bertha"Fontana, R. D. B."https://www.zbmath.org/authors/?q=ai:fontana.rodrigo-d-b"de Oliveira, Jeferson"https://www.zbmath.org/authors/?q=ai:de-oliveira.jefersonSummary: We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in 4 and \(D\) dimensions, respectively.Massive photons and electrically charged black holeshttps://www.zbmath.org/1475.830632022-01-14T13:23:02.489162Z"Dolgov, A. D."https://www.zbmath.org/authors/?q=ai:dolgov.alexandre-dmitrievich"Gudkova, K. S."https://www.zbmath.org/authors/?q=ai:gudkova.k-sSummary: The characteristic time of disappearance of electric field in massive electrodynamics during the capture of electric charge by black holes is calculated. It is shown that this time does not depend upon the photon mass. The electric field at large distances disappears with the speed of light.Classification and basic properties of circular orbits around regular black holes and solitons with the de Sitter centerhttps://www.zbmath.org/1475.830642022-01-14T13:23:02.489162Z"Dymnikova, Irina"https://www.zbmath.org/authors/?q=ai:dymnikova.irina-gavriilovna"Poszwa, Anna"https://www.zbmath.org/authors/?q=ai:poszwa.annaLosing the IR: a holographic framework for area theoremshttps://www.zbmath.org/1475.830652022-01-14T13:23:02.489162Z"Engelhardt, Netta"https://www.zbmath.org/authors/?q=ai:engelhardt.netta"Fischetti, Sebastian"https://www.zbmath.org/authors/?q=ai:fischetti.sebastianParticle collisions near static spherically symmetric black holeshttps://www.zbmath.org/1475.830672022-01-14T13:23:02.489162Z"Hackmann, Eva"https://www.zbmath.org/authors/?q=ai:hackmann.eva"Nandan, Hemwati"https://www.zbmath.org/authors/?q=ai:nandan.hemwati"Sheoran, Pankaj"https://www.zbmath.org/authors/?q=ai:sheoran.pankajSummary: It has been shown by Bañados, Silk and West (BSW) that the center of mass energy (\(E_{\mathrm{cm}}\)) of test particles starting from rest at infinity and colliding near the horizon of a Schwarzschild black hole is always finite. In this short note, we extent the BSW scenario and study two particles with different energies colliding near the horizon of a static spherically symmetric black hole. Interestingly, we find that even for the static spherically symmetric (i.e., Schwarzschild like) black holes it is possible to obtain an arbitrarily high \(E_{\mathrm{cm}}\) from the two test particles colliding near but outside of the horizon of a black hole, if one fine-tunes the parameters of geodesic motion.What black holes have taught us about quantum gravityhttps://www.zbmath.org/1475.830682022-01-14T13:23:02.489162Z"Harlow, Daniel"https://www.zbmath.org/authors/?q=ai:harlow.danielSummary: In this article I review the reasons why gravity has proven much more difficult to quantize than the other forces. Primary among them is the existence of black holes, whose remarkable properties tell us that a theory of quantum gravity must have a mathematical structure that is quite different from the quantum field theories that describe the rest of particle physics. These observations motivated the introduction of the `holographic principle', which argues that the fundamental degrees of freedom in a gravitational theory must live in a lower number of dimensions than the general relativity theory that it reduces to at low energies. The AdS/CFT correspondence gave the first sharp example of how this can be possible, and more recently several `toy models' of this correspondence have been introduced that clearly illustrate not just how holography can be realized but also why it must be. This article gives an overview of these recent developments.
For the entire collection see [Zbl 1460.81001].Holographic heat engines, entanglement entropy, and renormalization group flowhttps://www.zbmath.org/1475.830712022-01-14T13:23:02.489162Z"Johnson, Clifford V."https://www.zbmath.org/authors/?q=ai:johnson.clifford-v"Rosso, Felipe"https://www.zbmath.org/authors/?q=ai:rosso.felipe4D Einstein-Gauss-Bonnet gravity: massless particles and absorption of planar spin-0 waveshttps://www.zbmath.org/1475.830732022-01-14T13:23:02.489162Z"Junior, Haroldo C. D. Lima"https://www.zbmath.org/authors/?q=ai:haroldo-c-d-lima-jun."Benone, Carolina L."https://www.zbmath.org/authors/?q=ai:benone.carolina-l"Crispino, Luís C. B."https://www.zbmath.org/authors/?q=ai:crispino.luis-c-bSummary: We investigate the absorption cross section of planar scalar massless waves impinging on spherically symmetric black holes which are solutions of the novel 4D Einstein-Gauss-Bonnet theory of gravity. Besides the mass of the black hole, the solution depends also on the Gauss-Bonnet constant coupling. Using the partial waves approach, we show that the absorption cross section depends on the Gauss-Bonnet coupling constant. Our numerical results present excellent agreement with the low- and high-frequency approximations, including the so-called sinc approximation.Black hole enthalpy and scalar fieldshttps://www.zbmath.org/1475.830742022-01-14T13:23:02.489162Z"Kastor, David"https://www.zbmath.org/authors/?q=ai:kastor.david-a"Ray, Sourya"https://www.zbmath.org/authors/?q=ai:ray.sourya"Traschen, Jennie"https://www.zbmath.org/authors/?q=ai:traschen.jennieGrey-body factors and Hawking radiation of black holes in \(4D\) Einstein-Gauss-Bonnet gravityhttps://www.zbmath.org/1475.830752022-01-14T13:23:02.489162Z"Konoplya, Roman A."https://www.zbmath.org/authors/?q=ai:konoplya.roman-a"Zinhailo, Antonina F."https://www.zbmath.org/authors/?q=ai:zinhailo.antonina-fSummary: The \((3 + 1)\)-dimensional Einstein-Gauss-Bonnet theory of gravity which breaks the Lorentz invariance in a theoretically consistent and observationally viable way has been recently suggested by \textit{K. Aoki} et al. [Phys. Lett., B 810, Article ID 135843, 6 p. (2020; Zbl 1475.83119)]. Here we calculate grey-body factor for Dirac, electromagnetic and gravitational fields and estimate the intensity of Hawking radiation and lifetime for asymptotically flat black holes in this theory. Positive coupling constant leads to much smaller evaporation rate and longer life-time of a black hole, while the negative one enhances Hawking radiation. The grey-body factors for electromagnetic and Dirac fields are smaller for larger values of the coupling constant.Thermodynamic curvature of the Schwarzschild-AdS black hole and Bose condensationhttps://www.zbmath.org/1475.830782022-01-14T13:23:02.489162Z"Mahish, Sandip"https://www.zbmath.org/authors/?q=ai:mahish.sandip"Ghosh, Aritra"https://www.zbmath.org/authors/?q=ai:ghosh.aritra"Bhamidipati, Chandrasekhar"https://www.zbmath.org/authors/?q=ai:bhamidipati.chandrasekharSummary: In the AdS/CFT correspondence, a dynamical cosmological constant \(\Lambda\) in the bulk corresponds to varying the number of colors \(N\) in the boundary gauge theory with a chemical potential \(\mu\) as its thermodynamic conjugate. In this work, within the context of Schwarzschild black holes in \(AdS_5 \times S^5\) and its dual finite temperature \(\mathcal{N} = 4\) superconformal Yang-Mills theory at large \(N\), we investigate thermodynamic geometry through the behavior of the Ruppeiner scalar \(R\). The sign of \(R\) is an empirical indicator of the nature of microscopic interactions and is found to be negative for the large black hole branch implying that its thermodynamic characteristics bear qualitative similarities with that of an attraction dominated system, such as an ideal gas of bosons. We find that as the system's fugacity approaches unity, \(R\) takes increasingly negative values signifying long range correlations and strong quantum fluctuations signaling the onset of Bose condensation. On the other hand, \(R\) for the small black hole branch is negative at low temperatures and positive at high temperatures with a second order critical point which roughly separates the two regions.Speed limit of quantum dynamics near the event horizon of black holeshttps://www.zbmath.org/1475.830792022-01-14T13:23:02.489162Z"Maleki, Yusef"https://www.zbmath.org/authors/?q=ai:maleki.yusef"Maleki, Alireza"https://www.zbmath.org/authors/?q=ai:maleki.alirezaSummary: Quantum mechanics imposes a fundamental bound on the minimum time required for the quantum systems to evolve between two states of interest. This bound introduces a limit on the speed of the dynamical evolution of the systems, known as the quantum speed limit. We show that black holes can drastically affect the speed limit of a fermionic quantum system subjected to an open quantum dynamics. As we demonstrate, the quantum speed limit can enhance at the vicinity of a black hole's event horizon in the Schwarzschild spacetime.Evidence for the existence of a novel class of supersymmetric black holes with \(\mathrm{AdS}_5 \times \mathrm{S}^5\) asymptoticshttps://www.zbmath.org/1475.830802022-01-14T13:23:02.489162Z"Markevičiūtė, Julija"https://www.zbmath.org/authors/?q=ai:markeviciute.julija"Santos, Jorge E."https://www.zbmath.org/authors/?q=ai:santos.jorge-eExact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theoryhttps://www.zbmath.org/1475.830812022-01-14T13:23:02.489162Z"Momeni, Davood"https://www.zbmath.org/authors/?q=ai:momeni.davoodSummary: We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum \(p\) according to a quantum number \(n\). To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.Quantum fields in the background spacetime of a polymeric loop black holehttps://www.zbmath.org/1475.830822022-01-14T13:23:02.489162Z"Moulin, Flora"https://www.zbmath.org/authors/?q=ai:moulin.flora"Martineau, Killian"https://www.zbmath.org/authors/?q=ai:martineau.killian"Grain, Julien"https://www.zbmath.org/authors/?q=ai:grain.julien"Barrau, Aurélien"https://www.zbmath.org/authors/?q=ai:barrau.aurelienStudy of semiclassical instability of the Schwarzschild AdS black hole in the large \(D\) limithttps://www.zbmath.org/1475.830902022-01-14T13:23:02.489162Z"Sadhu, Amruta"https://www.zbmath.org/authors/?q=ai:sadhu.amruta"Suneeta, Vardarajan"https://www.zbmath.org/authors/?q=ai:suneeta.vardarajanWhy black hole information loss is paradoxicalhttps://www.zbmath.org/1475.830982022-01-14T13:23:02.489162Z"Wallace, David"https://www.zbmath.org/authors/?q=ai:wallace.david-james|wallace.david-alexander-ross|wallace.davidSummary: I distinguish between two versions of the black hole information-loss paradox. The first arises from apparent failure of unitarity on the spacetime of a completely evaporating black hole, which appears to be non-globally hyperbolic; this is the most commonly discussed version of the paradox in the foundational and semipopular literature, and the case for calling it ``paradoxical'' is less than compelling. But the second arises from a clash between a fully statistical-mechanical interpretation of black hole evaporation and the quantum-field-theoretic description used in derivations of the Hawking effect. This version of the paradox arises long before a black hole completely evaporates, seems to be the version that has played a central role in quantum gravity, and is genuinely paradoxical. After explicating the paradox, I discuss the implications of more recent work on AdS/CFT duality and on the ``Firewall paradox'', and conclude that the paradox is if anything now sharper. The article is written at a (relatively) introductory level and does not assume advanced knowledge of quantum gravity.
For the entire collection see [Zbl 1460.81001].Scalar field quasinormal modes of noncommutative high dimensional Schwarzschild-Tangherlini black hole spacetime with smeared matter sourceshttps://www.zbmath.org/1475.831032022-01-14T13:23:02.489162Z"Yan, Zening"https://www.zbmath.org/authors/?q=ai:yan.zening"Wu, Chen"https://www.zbmath.org/authors/?q=ai:wu.chen"Guo, Wenjun"https://www.zbmath.org/authors/?q=ai:guo.wenjunSummary: We investigate the massless scalar quasinormal modes (QNMs) of the noncommutative \(D\)-dimensional Schwarzschild-Tangherlini black hole spacetime in this paper. By using the Wentzel-Kramers-Brillouin (WKB) approximation method, the asymptotic iterative method (AIM) and the inverted potential method (IPM), we made a detail analysis of the massless scalar QNM frequencies by varying the general smeared matter distribution and the allowable characteristic parameters (\(k\) and \(\theta\)) corresponding to different dimensions. It is found that the nonconvergence of the high order WKB approximation exists in the QNMs frequencies of scalar perturbation around the noncommutative \(D\)-dimensional Schwarzschild black holes. We conclude that the 3rd WKB result should be more reliable than those of the high order WKB method since our numerical results are also verified by the AIM method and the IPM method. In the dimensional range of \(4 \leq D \leq 7\), the scalar QNMs as a function of the different parameters (the noncommutative parameter \(\theta \), the smeared matter distribution parameter \(k\), the multipole number \(l\) and the main node number \(n\)) are obtained. Moreover, we study the dynamical evolution of a scalar field in the background of the noncommutative high dimensional Schwarzschild-Tangherlini black hole.JT gravity and the asymptotic Weil-Petersson volumehttps://www.zbmath.org/1475.831082022-01-14T13:23:02.489162Z"Kimura, Yusuke"https://www.zbmath.org/authors/?q=ai:kimura.yusukeSummary: A path integral in Jackiw-Teitelboim (JT) gravity is given by integrating over the volume of the moduli of Riemann surfaces with boundaries, known as the ``Weil-Petersson volume,'' together with integrals over wiggles along the boundaries. The exact computation of the Weil-Petersson volume \(V_{g, n}(b_1, \dots, b_n)\) is difficult when the genus \(g\) becomes large. We utilize two partial differential equations known to hold on the Weil-Petersson volumes to estimate asymptotic behaviors of the volume with two boundaries \(V_{g, 2}(b_1, b_2)\) and the volume with three boundaries \(V_{g, 3}(b_1, b_2, b_3)\) when the genus \(g\) is large. Furthermore, we present a conjecture on the asymptotic expression for general \(V_{g, n}(b_1, \dots, b_n)\) with \(n\) boundaries when \(g\) is large.Towards the determination of the dimension of the critical surface in asymptotically safe gravityhttps://www.zbmath.org/1475.831122022-01-14T13:23:02.489162Z"Falls, Kevin"https://www.zbmath.org/authors/?q=ai:falls.kevin"Ohta, Nobuyoshi"https://www.zbmath.org/authors/?q=ai:ohta.nobuyoshi"Percacci, Roberto"https://www.zbmath.org/authors/?q=ai:percacci.robertoSummary: We compute the beta functions of Higher Derivative Gravity within the Functional Renormalization Group approach, going beyond previously studied approximations. We find that the presence of a nontrivial Newtonian coupling induces, in addition to the free fixed point of the one-loop approximation, also two nontrivial fixed points, of which one has the right signs to be free from tachyons. Our results are consistent with earlier suggestions that the dimension of the critical surface for pure gravity is three.Effect of torsion on the radiation fields in curved spacetimehttps://www.zbmath.org/1475.831152022-01-14T13:23:02.489162Z"Mandal, Susobhan"https://www.zbmath.org/authors/?q=ai:mandal.susobhanSummary: The torsion-free connection is one of the important assumptions in Einstein's General theory of Relativity which has not been verified so far from experimental observation. In this article, the effect of torsion on the on-shell action of radiation fields in curved spacetime is reported in order to show certain consequences and possible ways to probe torsion in curved spacetime. In order to describe non-vanishing torsion, we mostly use contorsion tensor in connection which can be written in the combination of torsion tensor and vice versa. We have discussed how does the field equation coming from the minimization of action \textit{with respect to} torsion changes the matter part of the on-shell action of radiation through substitution of the spin tensor. We have also studied here the effect of torsion on the scalar and vector radiation field in curved spacetime. It is shown that the presence of torsion leads to extra polarizations in Gravitational waves or radiations other than the usual two polarizations already present in General Relativity. Further, it is also shown that in the presence of torsion, there exists a non-trivial vacuum configuration that is different from the trivial vacuum in the absence of coupling with torsion. It is also found that in a generic theory of vector field, the presence of torsion breaks the \(U(1)\) gauge invariance just like the presence of mass shows the violation of gauge invariance. The observational consequences of these results are also discussed.Vacua in novel 4D Einstein-Gauss-Bonnet gravity: pathology and instability?https://www.zbmath.org/1475.831182022-01-14T13:23:02.489162Z"Shu, Fu-Wen"https://www.zbmath.org/authors/?q=ai:shu.fuwenSummary: We show an inconsistence of the novel 4D Einstein-Gauss-Bonnet gravity by considering a quantum tunneling process of vacua. Based on standard semiclassical techniques, we find a nonperturbative way to the study of the vacuum decay rate of the theory. We analytically compute all allowed cases in the parameter space. It turns out, without exception, that the theory either encounters a disastrous divergence of vacuum decay rate, or exhibits a confusing complex value of vacuum decay rate, or involves an instability (a large vacuum mixing). These suggest a strong possibility that the theory, at least the vacuum of the theory, is either unphysical or unstable, or has no well-defined limit as \(D \to 4\).A consistent theory of \(D \rightarrow 4\) Einstein-Gauss-Bonnet gravityhttps://www.zbmath.org/1475.831192022-01-14T13:23:02.489162Z"Aoki, Katsuki"https://www.zbmath.org/authors/?q=ai:aoki.katsuki"Gorji, Mohammad Ali"https://www.zbmath.org/authors/?q=ai:gorji.mohammad-ali"Mukohyama, Shinji"https://www.zbmath.org/authors/?q=ai:mukohyama.shinjiSummary: We investigate the \(D \to 4\) limit of the \(D\)-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with \(\tilde{\alpha} = (D - 4) \alpha\) kept fixed and \(\alpha\) is the original Gauss-Bonnet coupling. Using the ADM decomposition in \(D\) dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined) and depends on the way how to regularize the Hamiltonian or/and the equations of motion. To find a consistent theory in 4 dimensions that is different from general relativity, the regularization needs to either break (a part of) the diffeomorphism invariance or lead to an extra degree of freedom, in agreement with the Lovelock theorem. We then propose a consistent theory of \(D \to 4\) Einstein-Gauss-Bonnet gravity with two dynamical degrees of freedom by breaking the temporal diffeomorphism invariance and argue that, under a number of reasonable assumptions, the theory is unique up to a choice of a constraint that stems from a temporal gauge condition.Anomalous \(U(1)\) gauge bosons as light dark matter in string theoryhttps://www.zbmath.org/1475.831202022-01-14T13:23:02.489162Z"Anchordoqui, Luis A."https://www.zbmath.org/authors/?q=ai:anchordoqui.luis-alfredo"Antoniadis, Ignatios"https://www.zbmath.org/authors/?q=ai:antoniadis.ignatios"Benakli, Karim"https://www.zbmath.org/authors/?q=ai:benakli.karim"Lüst, Dieter"https://www.zbmath.org/authors/?q=ai:lust.dieterSummary: Present experiments are sensitive to very weakly coupled extra gauge symmetries which motivates further investigation of their appearance in string theory compactifications and subsequent properties. We consider extensions of the standard model based on open strings ending on D-branes, with gauge bosons due to strings attached to stacks of D-branes and chiral matter due to strings stretching between intersecting D-branes. Assuming that the fundamental string mass scale saturates the current LHC limit and that the theory is weakly coupled, we show that (anomalous) \(U(1)\) gauge bosons which propagate into the bulk are compelling light dark matter candidates. We comment on the possible relevance of the \(U(1)\) gauge bosons, which are universal in intersecting D-brane models, to the observed \(3 \sigma\) excess in XENON1T.Spacetime and physical equivalencehttps://www.zbmath.org/1475.831212022-01-14T13:23:02.489162Z"De Haro, Sebastian"https://www.zbmath.org/authors/?q=ai:de-haro.sebastianSummary: String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in this chapter that those two conspicuous characteristics of string physics are related to each other. What links them together is the fact that string theory has no dimensionless-free parameters at a fundamental level. The paper analyzes possible implications of this situation for the long-term prospects of theory building in fundamental physics.
For the entire collection see [Zbl 1460.81001].Black remnants from T-dualityhttps://www.zbmath.org/1475.831222022-01-14T13:23:02.489162Z"Pourhassan, Behnam"https://www.zbmath.org/authors/?q=ai:pourhassan.behnam"Wani, Salman Sajad"https://www.zbmath.org/authors/?q=ai:wani.salman-sajad"Faizal, Mir"https://www.zbmath.org/authors/?q=ai:faizal.mirSummary: In this paper, we will analyze the physical consequences of black remnants, which form due to non-perturbative string theoretical effects. These non-perturbative effects occur due to the T-duality in string theory. We will analyze the production of such black remnants in models with large extra dimensions, and demonstrate that these non-perturbative effects can explain the absence of mini black holes at the LHC. In fact, we will constraint such models using data from the LHC. We will also analyze such non-perturbative corrections for various other black hole solutions. Thus, we will analyze the effects of such non-perturbative corrections on the Van der Waals behavior of AdS black holes. We will also discuss the effects of adding a chemical potential to this system. Finally, we will comment on the physical consequences of such non-perturbative corrections to black hole solutions.On effective field theory of F-theory beyond leading orderhttps://www.zbmath.org/1475.831232022-01-14T13:23:02.489162Z"Bakhtiarizadeh, Hamid R."https://www.zbmath.org/authors/?q=ai:bakhtiarizadeh.hamid-rThe structure of all the supersymmetric solutions of ungauged \(\mathcal{N}=(1,0)\), \(d=6\) supergravityhttps://www.zbmath.org/1475.831242022-01-14T13:23:02.489162Z"Cano, Pablo A."https://www.zbmath.org/authors/?q=ai:cano.pablo-a"Ortín, Tomás"https://www.zbmath.org/authors/?q=ai:ortin.tomasGeneralised Garfinkle-Vachaspati transform with dilatonhttps://www.zbmath.org/1475.831252022-01-14T13:23:02.489162Z"Chakrabarti, Subhroneel"https://www.zbmath.org/authors/?q=ai:chakrabarti.subhroneel"Mishra, Deepali"https://www.zbmath.org/authors/?q=ai:mishra.deepali"Srivastava, Yogesh K."https://www.zbmath.org/authors/?q=ai:srivastava.yogesh-k"Virmani, Amitabh"https://www.zbmath.org/authors/?q=ai:virmani.amitabhChoices of spinor inner products on m-theory backgroundshttps://www.zbmath.org/1475.831262022-01-14T13:23:02.489162Z"Ertem, Ümit"https://www.zbmath.org/authors/?q=ai:ertem.umit"Sütemen, Özgün"https://www.zbmath.org/authors/?q=ai:sutemen.ozgun"Açık, Özgür"https://www.zbmath.org/authors/?q=ai:acik.ozgur"Çatalkaya, Aytolun"https://www.zbmath.org/authors/?q=ai:catalkaya.aytolunSummary: M-theory backgrounds in the form of unwarped compactifications with or without fluxes are considered. We construct the bilinear forms of supergravity Killing spinors for different choices of spinor inner products on these backgrounds. The equations satisfied by the bilinear forms and their decompositions into product manifolds are obtained for different inner product choices in the special case for which the spinors factorize. It is found that the \textit{AdS} solutions can only appear for some special choices of spinor inner products on product manifolds. The reduction of bilinears of supergravity Killing spinors into the hidden symmetries of product manifolds which are Killing-Yano and closed conformal Killing-Yano forms for \textit{AdS} solutions is shown. These hidden symmetries are lifted to eleven-dimensional backgrounds to find the hidden symmetries on them. The relation between the choices of spinor inner products, \textit{AdS} solutions and hidden symmetries on M-theory backgrounds are investigated.Polymer quantum mechanics as a deformation quantizationhttps://www.zbmath.org/1475.831282022-01-14T13:23:02.489162Z"Berra-Montiel, Jasel"https://www.zbmath.org/authors/?q=ai:berra-montiel.jasel"Molgado, Alberto"https://www.zbmath.org/authors/?q=ai:molgado.albertoNon-minimally coupled quartic inflation with Coleman-Weinberg one-loop corrections in the Palatini formulationhttps://www.zbmath.org/1475.831292022-01-14T13:23:02.489162Z"Bostan, Nilay"https://www.zbmath.org/authors/?q=ai:bostan.nilaySummary: We discuss how the non-minimal coupling \(\xi \phi^2 R\) between the inflaton and the Ricci scalar affects the predictions of single field inflation models in the Palatini formalism. The inflaton field \(\phi\) must interact with matter fields at the end of inflation in order to make a transition to the radiation dominated era. Interactions of the inflaton with other fields lead to radiative corrections to the inflationary potential. These radiative corrections can be explained at leading order by Coleman-Weinberg (CW) one-loop corrections. In this work, the effect of radiative corrections to the potential has been examined using two different prescriptions debated in the literature. Prescription I and Prescription II examine the coupling of the inflaton to bosons and fermions. We analyze the range of these coupling parameters for which the spectral index \(n_s\) and the tensor-to-scalar ratio \(r\) are compatible with data taken by the Keck Array/BICEP2 and Planck collaborations. Finally, we show for all the considered potentials the behavior of the running of the spectral index \(\alpha = \mathrm{d} n_s / \mathrm{d} \ln k\) as a function of \(\kappa\) for selected \(\xi\) values.Conformal unification in a quiver theory and gravitational waveshttps://www.zbmath.org/1475.831312022-01-14T13:23:02.489162Z"Corianò, Claudio"https://www.zbmath.org/authors/?q=ai:coriano.claudio"Frampton, Paul H."https://www.zbmath.org/authors/?q=ai:frampton.paul-howard"Tatullo, Alessandro"https://www.zbmath.org/authors/?q=ai:tatullo.alessandroSummary: The detection of a stochastic background of gravitational waves can reveal details about first-order phase transitions (FOPTs) at a time of \(10^{-13}\) s of the early universe. We specifically discuss quiver-type GUTs which avoid both proton decay and a desert hypothesis. A quiver based on \(SU(3)^{12}\) which breaks at a \(E = 4000\) GeV to trinification \(SU(3)^3\) has a much larger (\(g_\ast = 1,272\)) number of effective massless degrees of freedom than the Standard Model. Assuming a FOPT for this model, we investigate the strain sensitivity of typical of this model for a wide range of FOPT parameters.Effective field theory of dark energy: a reviewhttps://www.zbmath.org/1475.831342022-01-14T13:23:02.489162Z"Frusciante, Noemi"https://www.zbmath.org/authors/?q=ai:frusciante.noemi"Perenon, Louis"https://www.zbmath.org/authors/?q=ai:perenon.louisSummary: The discovery of cosmic acceleration has triggered a consistent body of theoretical work aimed at modeling its phenomenology and understanding its fundamental physical nature. In recent years, a powerful formalism that accomplishes both these goals has been developed, the so-called effective field theory of dark energy. It can capture the behavior of a wide class of modified gravity theories and classify them according to the imprints they leave on the smooth background expansion history of the Universe and on the evolution of linear perturbations. The effective field theory of dark energy is based on a Lagrangian description of cosmological perturbations which depends on a number of functions of time, some of which are non-minimal couplings representing genuine deviations from General Relativity. Such a formalism is thus particularly convenient to fit and interpret the wealth of new data that will be provided by future galaxy surveys. Despite its recent appearance, this formalism has already allowed a systematic investigation of what lies beyond the General Relativity landscape and provided a conspicuous amount of theoretical predictions and observational results. In this review, we report on these achievements.Kaluza-Klein modes of \(U(1)\) gauge vector field on brane with codimension-\(d\)https://www.zbmath.org/1475.831352022-01-14T13:23:02.489162Z"Fu, Chun-E"https://www.zbmath.org/authors/?q=ai:fu.chun-e"Zhong, Yuan"https://www.zbmath.org/authors/?q=ai:zhong.yuan"Guo, Heng"https://www.zbmath.org/authors/?q=ai:guo.heng"Zhao, Li"https://www.zbmath.org/authors/?q=ai:zhao.li"Chen, Zi-Qi"https://www.zbmath.org/authors/?q=ai:chen.ziqiSummary: From the paper of the first two authors et al. [J. High Energy Phys. 2019, No. 1, Paper No. 21, 16 p. (2019; Zbl 1409.81096)] it is known that the effective action of a massless \(U(1)\) gauge vector field on a codimension-2 brane is gauge invariant due to the coupling between the vector Kaluza-Klein (KK) modes with two types of scalar KK modes. It is interesting to generalize this result to a brane world model with an arbitrary number of extra dimensions. In this work, we first investigate the case with three extra dimensions. After KK decomposition, there are three types of scalar KK modes. In addition to the mutual coupling between these scalar modes, there are also coupling between the scalar and the vector KK modes. The coupling constants are not all independent. The relationships between the coupling constants enable us to obtain a gauge invariant effective action, from which we can see that the masses of the vector KK modes are contributed by all the three extra dimensions. The masses of the scalar modes, however, are contributed only by two of the three extra dimensions. Then we generalize our results to branes with codimension \(d\) (\(d = 1, 2\dots\)).An interacting fermion-antifermion pair in the spacetime background generated by static cosmic stringhttps://www.zbmath.org/1475.831392022-01-14T13:23:02.489162Z"Guvendi, Abdullah"https://www.zbmath.org/authors/?q=ai:guvendi.abdullah"Sucu, Yusuf"https://www.zbmath.org/authors/?q=ai:sucu.yusufSummary: We consider a general relativistic fermion antifermion pair that they interact via an attractive Coulomb type interparticle interaction potential in the \(2 + 1\) dimensional spacetime background spanned by cosmic string. By performing an exact solution of the corresponding fully-covariant two body Dirac Coulomb type equation we obtain an energy spectrum that depends on angular deficit parameter of the static cosmic string spacetime background for such a composite system. We arrive that the influence of cosmic string spacetime topology on the binding energy of Positronium-like atoms can be seen in all order of the coupling strength constant, even in the well-known non-relativistic binding energy term (\(\propto \alpha_c^2\)). We obtain that the angular deficit of the static cosmic string spacetime background causes a screening effect. For a predicted value of angular deficit parameter, \(\alpha \sim\) 1--\(10^{-6}\), we apply the obtained result to an ortho-positronium, which is an unstable atom formed by an electron and its antimatter counterpart a positron, and then we determine the shift in the ground state binding energy level as 27, 2 \micro eV. We also arrive that, in principle, the shift in ground state binding energy of ortho-positronium can be measured even for \(\alpha \sim\) 1--\(10^{-11}\) value with current techniques in use today. Moreover, this also gives us an opportunity to determine the altered total annihilation energy transmitted by the annihilation photons. The yields also impose that the total lifetime of an ortho-positronium can be changed by the topological feature of static cosmic string spacetime background. In principle, we show that an ortho-positronium system has a potential to prove the existence of such a spacetime background.Spin Hall effect of light in inhomogeneous axion fieldhttps://www.zbmath.org/1475.831402022-01-14T13:23:02.489162Z"Hoseini, Mansoureh"https://www.zbmath.org/authors/?q=ai:hoseini.mansoureh"Mehrafarin, Mohammad"https://www.zbmath.org/authors/?q=ai:mehrafarin.mohammadSummary: We study the spin transport of light in weakly inhomogeneous axion field in a flat Robertson-Walker universe and derive the spin Hall effect for circularly polarized rays. Regarding primordial quantum fluctuations of the axion field in the de Sitter phase as the origin of the inhomogeneity, we show that the conformal invariance of the correlator determines the root-mean-square (r.m.s) fluctuation of the path of circularly polarized cosmic rays. We explain how the r.m.s fluctuation can be experimentally determined.Influence of intrinsic spin in the formation of singularities for inhomogeneous effective dust space-timeshttps://www.zbmath.org/1475.831412022-01-14T13:23:02.489162Z"Luz, Paulo"https://www.zbmath.org/authors/?q=ai:luz.paulo"Mena, Filipe C."https://www.zbmath.org/authors/?q=ai:mena.filipe-c"Hadi Ziaie, Amir"https://www.zbmath.org/authors/?q=ai:ziaie.amir-hadiHolographic dual of the weak gravity conjecturehttps://www.zbmath.org/1475.831422022-01-14T13:23:02.489162Z"McInnes, Brett"https://www.zbmath.org/authors/?q=ai:mcinnes.brettSummary: The much-discussed \textit{Weak Gravity Conjecture} is interesting and important in both the asymptotically flat and the asymptotically AdS contexts. In the latter case, it is natural to ask what conditions it (and the closely related Cosmic Censorship principle) imposes, via gauge-gravity duality, on the boundary field theory. We find that these conditions take the form of lower bounds on the number of colours in this theory: that is, the WGC and Censorship might (depending on the actual sizes of the bounds) enforce the familiar holographic injunction that this number should be ``large''. We explicitly estimate lower bounds on this number in the case of the application of holography to the quark-gluon plasma produced in heavy ion collisions. We find that classical Censorship alone prohibits realistically small values for the number of colours, but that the WGC offers hope of resolving this problem.A domain wall description of brane inflation and observational aspectshttps://www.zbmath.org/1475.831432022-01-14T13:23:02.489162Z"Neves, R. M. P."https://www.zbmath.org/authors/?q=ai:neves.r-m-p"Santos, F. F."https://www.zbmath.org/authors/?q=ai:santos.f-f"Brito, F. A."https://www.zbmath.org/authors/?q=ai:brito.fabrito-a|brito.francisco-aSummary: We consider a brane cosmology scenario by taking an inflating 3D domain wall immersed in a five-dimensional Minkowski space in the presence of a stack of \(N\) parallel domain walls. They are static BPS solutions of the bosonic sector of a 5D supergravity theory. However, one can move towards each other due to an attractive force in between driven by bulk particle collisions and \textit{resonant tunneling effect}. The accelerating domain wall is a 3-brane that is assumed to be our inflating early Universe. We analyze this inflationary phase governed by the inflaton potential induced on the brane. We compute the slow-roll parameters and show that the spectral index and the tensor-to-scalar ratio are within the recent observational data.Erratum to: ``Is there a super-selection rule in quantum cosmology?''https://www.zbmath.org/1475.831462022-01-14T13:23:02.489162Z"Santini, E. Sergio"https://www.zbmath.org/authors/?q=ai:santini.eduardo-sergioA small graphic error in the author's paper [ibid. 25, No. 3, 226--236 (2019; Zbl 1437.83170)] is corrected.Lemaître-Tolman-Bondi static universe in Rastall-like gravityhttps://www.zbmath.org/1475.831512022-01-14T13:23:02.489162Z"Yu, Zhong-Xi"https://www.zbmath.org/authors/?q=ai:yu.zhong-xi"Li, Shou-Long"https://www.zbmath.org/authors/?q=ai:li.shoulong"Wei, Hao"https://www.zbmath.org/authors/?q=ai:wei.haoSummary: In this work, we try to obtain a stable Lemaître-Tolman-Bondi (LTB) static universe, which is spherically symmetric and radially inhomogeneous. However, this is not an easy task, and fails in general relativity (GR) and various modified gravity theories, because the corresponding LTB static universes must reduce to the Friedmann-Robertson-Walker (FRW) static universes. We find a way out in a new type of modified gravity theory, in which the conservation of energy and momentum is broken. In this work, we have proposed a novel modification to the original Rastall gravity. In some sense, our Rastall-like gravity is essentially different from GR and the original Rastall gravity. In this Rastall-like gravity, LTB static solutions have been found. The stability of LTB static universe against both the homogeneous and the inhomogeneous scalar perturbations is also discussed in details. We show that a LTB static universe can be stable in this Rastall-like gravity.A Birman-Schwinger principle in galactic dynamicshttps://www.zbmath.org/1475.850022022-01-14T13:23:02.489162Z"Kunze, Markus"https://www.zbmath.org/authors/?q=ai:kunze.markus-christian|kunze.markusOne of the simplest versions of the Birman-Schwinger principle is that a negative real number \(-e\) is an eigenvalue of the Schrödinger operator \(H:=-\Delta+V\) acting in \(L^2(\mathbb{R}^n)\) with the potential \(V\le 0\) if and only if \(1\) is an eigenvalue of the operator \(B_e:=\sqrt{-V}(-\Delta+e)^{-1}\sqrt{-V}\), and there are moreover simple formulas that relate the eigenfunctions of \(H\) and \(B_e\), respectively. The usefulness of this approach is due to the fact that the operator \(B_e\) is a nonnegative Hilbert-Schmidt operator under suitable decay hypothesies on the potential~\(V\). The book under review develops a version of the Birman-Schwinger principle which is applicable in certain stability problems of the non-relativistic galactic dynamics. As mentioned in the introductory chapter, the time evolution of self-gravitating matter is described by the Vlasov-Poisson system \(\partial_tf(t,x,v)+v\cdot\nabla_x f(t,x,v)-\nabla_xU_f(t,x)\cdot\nabla_vf(t,x,v)=0\), where \((t,x,v)\in \mathbb{R}\times\mathbb{R}^3\times\mathbb{R}^3\) and \(U_f(t,x)=-\int_{\mathbb{R}^3}\frac{\rho_f(t,y)}{\vert y-x\vert}dy\), while \(\rho_f(t,y)=\int_{\mathbb{R}^3}f(t,y,\cdot)\). Let \(Q=Q(x,v)\) be a steady state solution with the particle energy \(e_Q(x,v)=\frac{1}{2}\vert v\vert^2+U_Q(x)\), and define its corresponding operators \(g\mapsto \mathcal{T}g:=\{g,e_Q\}\) and \(g\mapsto \mathcal{K}g:=\{Q,U_g\}\), where \(\{\cdot,\cdot\}\) is the canonical Poisson bracket on \(\mathbb{R}^3\times\mathbb{R}^3\). One then proves that, under appropriate hypotheses on the steady state solution~\(Q\), the operator \(u\mapsto Lu:=-\mathcal{T}^2u-\mathcal{K}\mathcal{T}u\) is essentially selfadjoint and bounded from below with respect to a suitable inner product depending on~\(Q\) (Theorem 1.2). It is to that operator \(L\) that one associates a family of non-negative Hilbert-Schmidt operators \(\mathcal{Q}_\lambda\) with the properties similar to the operators \(B_e\) associated to the Schrödinger operator~\(H\). Using this approach, one can determine when the best constant in the Anosov stability estimate is attained (i.e., the aforementioned lower boundedness property of~\(L\)). The main body of the monograph contains the rigorous development of that approach, and there are also several appendices where the most technical details are treated.
Reviewer: Daniel Beltiţă (Bucureşti)A new consistent neutron star equation of state from a generalized Skyrme modelhttps://www.zbmath.org/1475.850052022-01-14T13:23:02.489162Z"Adam, Christoph"https://www.zbmath.org/authors/?q=ai:adam.christoph"Martín-Caro, Alberto García"https://www.zbmath.org/authors/?q=ai:martin-caro.alberto-garcia"Huidobro, Miguel"https://www.zbmath.org/authors/?q=ai:huidobro.miguel"Vázquez, Ricardo"https://www.zbmath.org/authors/?q=ai:vazquez.ricardo"Wereszczynski, Andrzej"https://www.zbmath.org/authors/?q=ai:wereszczynski.andrzejSummary: We propose a new equation of state for nuclear matter based on a generalized Skyrme model which is consistent with all current constraints on the observed properties of neutron stars. This generalized model depends only on two free parameters related to the ranges of pressure values at which different submodels are dominant, and which can be adjusted so that mass-radius and deformability constraints from astrophysical and gravitational wave measurements can be met. Our results support the Skyrme model and its generalizations as good candidates for a low energy effective field-theoretic description of nuclear matter even at extreme conditions such as those inside neutron stars.Radial oscillations of boson stars made of ultralight repulsive dark matterhttps://www.zbmath.org/1475.850092022-01-14T13:23:02.489162Z"Lopes, Ilídio"https://www.zbmath.org/authors/?q=ai:lopes.ilidio"Panotopoulos, Grigoris"https://www.zbmath.org/authors/?q=ai:panotopoulos.grigorisSummary: We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales \(m\) (mass of the particle) and \(F\) (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schrödinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by \(\Lambda \equiv \sqrt{mF} \).Stellar structure models in modified theories of gravity: lessons and challengeshttps://www.zbmath.org/1475.850102022-01-14T13:23:02.489162Z"Olmo, Gonzalo J."https://www.zbmath.org/authors/?q=ai:olmo.gonzalo-j"Rubiera-Garcia, Diego"https://www.zbmath.org/authors/?q=ai:rubiera-garcia.diego"Wojnar, Aneta"https://www.zbmath.org/authors/?q=ai:wojnar.anetaSummary: The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of the strong field regime of General Relativity, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its principles. These theories typically change the Tolman-Oppenheimer-Volkoff equations of stellar's hydrostatic equilibrium, thus having a large impact on the astrophysical properties of the corresponding stars and opening a new window to constrain these theories with present and future observations of different types of stars. For relativistic stars, such as neutron stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters coming from the modified gravity side, providing a whole new phenomenology for the typical predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars, such as white, brown and red dwarfs, the weakening/strengthening of the gravitational force inside astrophysical bodies via the modified Newtonian (Poisson) equation may induce changes on the star's mass, radius, central density or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning in high-mass brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature for many such modified theories of gravity, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modelings, and observational aspects, highlighting some of the most promising opportunities in the field.Massive compact Bardeen stars with conformal motionhttps://www.zbmath.org/1475.850122022-01-14T13:23:02.489162Z"Shamir, M. Farasat"https://www.zbmath.org/authors/?q=ai:shamir.m-farasatSummary: The main focus of this paper is to discuss the solutions of Einstein-Maxwell's field equations for compact stars study. We have chosen the MIT Bag model equation of state for the pressure-energy density relationship and conformal Killing vectors are used to investigate the appropriate forms for metric coefficients. We impose the boundary conditions, by choosing the Bardeen model to describe as an exterior spacetime. The Bardeen model may provide the analysis with some interesting results. For example, the extra terms involved in the asymptotic representations as compared to the usual Reissner-Nordstrom case may influence the mass of a stellar structure. Both energy density and pressure profiles behave realistically except a central singularity. It is shown that the energy conditions are satisfied in our study. The equilibrium conditions through TOV equation and stability criteria through Adiabatic index for the charged stellar structure study are investigated. We have also provided a little review of the case with Reissner-Nordstrom spacetime as an exterior geometry for the matching condition. In both cases, the masses obey the Andreasson's limit \(\sqrt{ M} \leq \sqrt{ R} / 3 + \sqrt{ R / 9 + q^2 / 3 R}\) requirement for a charged star. Conclusively, the results show that Bardeen model geometry provides more massive stellar objects as compared to usual Reissner-Nordstrom spacetime. In particular, the current study supports the existence of realistic massive structures like PSR J \(1614-2230\).Asymptotic normalization coefficient method for two-proton radiative capturehttps://www.zbmath.org/1475.850132022-01-14T13:23:02.489162Z"Grigorenko, L. V."https://www.zbmath.org/authors/?q=ai:grigorenko.l-v"Parfenova, Yu. L."https://www.zbmath.org/authors/?q=ai:parfenova.yu-l"Shulgina, N. B."https://www.zbmath.org/authors/?q=ai:shulgina.n-b"Zhukov, M. V."https://www.zbmath.org/authors/?q=ai:zhukov.maxim-valerievichSummary: The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body \(2p\) radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture \(^{15}\mathrm{O}+ p + p \to{}^{17}\mathrm{Ne} + \gamma\) is considered as an illustration.DFSZ axion couplings revisitedhttps://www.zbmath.org/1475.850142022-01-14T13:23:02.489162Z"Sun, Jin"https://www.zbmath.org/authors/?q=ai:sun.jin"He, Xiao-Gang"https://www.zbmath.org/authors/?q=ai:he.xiao-gangSummary: Among many possibilities, solar axion has been proposed to explain the electronic recoil events excess observed by Xenon1T collaboration, although it has tension with astrophysical observations. The axion couplings, to photon \(g_{a\gamma}\) and to electron \(g_{ae}\) play important roles. These couplings are related to the Peccei-Quinn (PQ) charges \(X_f\) for fermions. In most of the calculations, \( g_{a\gamma}\) is obtained by normalizing to the ratio of electromagnetic anomaly factor \(E = Tr X_f Q_f^2 N_c\) (\(N_c\) is 3 and 1 for quarks and charged leptons respectively) and QCD anomaly factor \(N = Tr X_q T(q)\) (\(T(q)\) is quarks' \(SU(3)_c\) index). The broken PQ symmetry generator is used in the calculation which does not seem to extract out the components of broken generator in the axion which are ``eaten'' by the \(Z\) boson. However, using the physical components of axion or the ratio of anomaly factors should obtain the same results in the DFSZ for \(g_{a\gamma}\). When going beyond the standard DFSZ models, such as variant DFSZ models, where more Higgs doublets and fermions have different PQ charges, one may wonder if the results are different. We show that the two methods obtain the same results as expected, but the axion couplings to quarks and leptons \(g_{af}\) (here f indicates one of the fermions in the SM) are more conveniently calculated in the physical axion basis. The result depends on the values of the vacuum expectation values leading to a wider parameter space for \(g_{af}\) in beyond the standard DFSZ axion. We also show explicitly how flavor conserving \(g_{af}\) couplings can be maintained when there are more than one Higgs doublets couple to the up and down fermion sectors in variant DFSZ models at tree level, and how flavor violating couplings can arise.Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral viewhttps://www.zbmath.org/1475.920802022-01-14T13:23:02.489162Z"Vastola, John J."https://www.zbmath.org/authors/?q=ai:vastola.john-jSummary: The chemical master equation (CME) is a fundamental description of interacting molecules commonly used to model chemical kinetics and noisy gene regulatory networks. Exact time-dependent solutions of the CME -- which typically consists of infinitely many coupled differential equations -- are rare, and are valuable for numerical benchmarking and getting intuition for the behavior of more complicated systems. \textit{T. Jahnke} and \textit{W. Huisinga}'s [J. Math. Biol. 54, No. 1, 1--26 (2007; Zbl 1113.92032)] landmark calculation of the exact time-dependent solution of the CME for monomolecular reaction systems is one of the most general analytic results known; however, it is hard to generalize, because it relies crucially on special properties of monomolecular reactions. In this paper, we rederive Jahnke and Huisinga's result on the time-dependent probability distribution and moments of monomolecular reaction systems using the Doi-Peliti path integral approach, which reduces solving the CME to evaluating many integrals. While the Doi-Peliti approach is less intuitive, it is also more mechanical, and hence easier to generalize. To illustrate how the Doi-Peliti approach can go beyond the method of Jahnke and Huisinga, we also find an explicit and exact time-dependent solution to a problem involving an autocatalytic reaction that Jahnke and Huisinga identified as not solvable using their method. Most interestingly, we are able to find a formal exact time-dependent solution for any CME whose list of reactions involves only zero and first order reactions, which may be the most general result currently known. This formal solution also yields a useful algorithm for efficiently computing numerical solutions to CMEs of this type.Classical capacities of memoryless but not identical quantum channelshttps://www.zbmath.org/1475.940702022-01-14T13:23:02.489162Z"Oskouei, Samad Khabbazi"https://www.zbmath.org/authors/?q=ai:oskouei.samad-khabbazi"Mancini, Stefano"https://www.zbmath.org/authors/?q=ai:mancini.stefanoOn the concept of quantum hashinghttps://www.zbmath.org/1475.940892022-01-14T13:23:02.489162Z"Ablayev, F. M."https://www.zbmath.org/authors/?q=ai:ablaev.farid-m"Ablayev, M. F."https://www.zbmath.org/authors/?q=ai:ablayev.m-fSummary: We present the notion of quantum hashing as a natural generalization of classical hashing. We suggest the concept of a quantum hash generator and a design allowing to construct a large number of different quantum hash functions.
The construction is based on composition of a classical \(\varepsilon \)-universal hash family and a given family of functions -- quantum hash generators.Round5: compact and fast post-quantum public-key encryptionhttps://www.zbmath.org/1475.941022022-01-14T13:23:02.489162Z"Baan, Hayo"https://www.zbmath.org/authors/?q=ai:baan.hayo"Bhattacharya, Sauvik"https://www.zbmath.org/authors/?q=ai:bhattacharya.sauvik"Fluhrer, Scott"https://www.zbmath.org/authors/?q=ai:fluhrer.scott-r"Garcia-Morchon, Oscar"https://www.zbmath.org/authors/?q=ai:garcia-morchon.oscar"Laarhoven, Thijs"https://www.zbmath.org/authors/?q=ai:laarhoven.thijs"Rietman, Ronald"https://www.zbmath.org/authors/?q=ai:rietman.ronald"Saarinen, Markku-Juhani O."https://www.zbmath.org/authors/?q=ai:saarinen.markku-juhani-olavi"Tolhuizen, Ludo"https://www.zbmath.org/authors/?q=ai:tolhuizen.ludo-m-g-m"Zhang, Zhenfei"https://www.zbmath.org/authors/?q=ai:zhang.zhenfeiSummary: We present the ring-based configuration of the NIST submission Round5, a Ring Learning with Rounding (RLWR)-based IND-CPA secure public-key encryption scheme. It combines elements of the NIST candidates Round2 (use of RLWR as underlying problem, having \(1+x+\ldots +x^n\) with \(n+1\) prime as reduction polynomial, allowing for a large design space) and HILA5 (the constant-time error-correction code XEf). Round5 performs part of encryption, and decryption via multiplication in \(\mathbb{Z}_p[x]/(x^{n+1}-1)\), and uses secret-key polynomials that have a factor \((x-1)\). This technique reduces the failure probability and makes correlation in the decryption error negligibly low. The latter allows the effective application of error correction through XEf to further reduce the failure rate and shrink parameters, improving both security and performance.
We argue for the security of Round5, both formal and concrete. We further analyze the decryption error, and give analytical as well as experimental results arguing that the decryption failure rate is lower than in Round2, with negligible correlation in errors.
IND-CCA secure parameters constructed using Round5 and offering more than 232 and 256 bits of quantum and classical security respectively, under the conservative core sieving model, require only 2144 B of bandwidth. For comparison, similar, competing proposals require over 30\% more bandwidth. Furthermore, the high flexilibity of Round5's design allows choosing finely tuned parameters fitting the needs of diverse applications -- ranging from the IoT to high-security levels.
For the entire collection see [Zbl 1418.94003].Application of non-associative structures to the construction of public key distribution algorithmshttps://www.zbmath.org/1475.941052022-01-14T13:23:02.489162Z"Baryshnikov, A. V."https://www.zbmath.org/authors/?q=ai:baryshnikov.a-v"Katyshev, S. Yu."https://www.zbmath.org/authors/?q=ai:katyshev.sergey-yuSummary: We explore the possibility of using non-associative groupoids to construct public key distribution algorithms generalizing the Diffie-Hellmann algorithm. A class of non-associative groupoids satisfying the power permutability property is founded. For this class the complexity of computing powers of an element and the complexity of discrete logarithm problem, including the possible usage of hypothetical quantum computer.Quantum attacks against iterated block ciphershttps://www.zbmath.org/1475.941252022-01-14T13:23:02.489162Z"Kaplan, M."https://www.zbmath.org/authors/?q=ai:kaplan.marc-a|kaplan.michael|kaplan.melike|kaplan.matthew-l|kaplan.m-d|kaplan.markSummary: We study the amplification of security against quantum attacks provided by iteration of block ciphers. We prove that (in contrast to the classical Meet-in-the-middle attack) for quantum adversaries two iterated ideal block ciphers are more much difficult to attack than a single one. The optimality of the quantized Meet-in-the-middle attack is proved. It is shown that contrary to the classical case, the quantum dissection attack against 4-encryption has a better time complexity than a quantum Meet-in-the-middle attack.New methods of error correction in quantum cryptography using low-density parity-check codeshttps://www.zbmath.org/1475.941302022-01-14T13:23:02.489162Z"Kronberg, D. A."https://www.zbmath.org/authors/?q=ai:kronberg.d-aSummary: The problem of error correction in quantum cryptography is considered, including the estimation of error rate. We show that low-density parity-check (LDPC) codes are appropriate for this problem, and propose some modifications to achieve better code performance, taking into account the special properties of quantum cryptography.