Recent zbMATH articles in MSC 81Uhttps://www.zbmath.org/atom/cc/81U2021-04-16T16:22:00+00:00WerkzeugBethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory.https://www.zbmath.org/1456.812412021-04-16T16:22:00+00:00"Kormos, M."https://www.zbmath.org/authors/?q=ai:kormos.marton"Mussardo, G."https://www.zbmath.org/authors/?q=ai:mussardo.guiseppe|mussardo.giuseppe"Pozsgay, B."https://www.zbmath.org/authors/?q=ai:pozsgay.balazsLorentz invariance violation and modified Hawking fermions tunneling radiation of stationary axially symmetric black holes.https://www.zbmath.org/1456.830452021-04-16T16:22:00+00:00"Luo, Z."https://www.zbmath.org/authors/?q=ai:luo.zhongling|luo.zeyu|luo.zhikang|luo.zhibo|luo.zhenghua|luo.zhaohui|luo.ziwei|luo.zhihuan|luo.zhiliang|luo.zhao|luo.zhicheng|luo.zhaoming|luo.zhusan|luo.zhiwen|luo.zhonghua|luo.zhe|luo.zhongxian|luo.zhiguo|luo.zhiwei|luo.zhenjiang|luo.zhongwen|luo.zhengxuan|luo.zongfu|luo.zhiming|luo.zhipeng|luo.zuojuan|luo.zhongjie|luo.zhongqiang|luo.zhaoyang|luo.zhifan|luo.zuying|luo.zhenbi|luo.zhongliang|luo.zhenou|luo.zhigang|luo.zhongxiang|luo.zhongde|luo.zhengming|luo.zhendong|luo.zujun|luo.zhongxuan|luo.zhong|luo.ziyan|luo.zhigo|luo.zhixue|luo.zhuangchu|luo.zuwen|luo.zhukai|luo.zhenjun|luo.zhi-quan|luo.zhengdong|luo.zhenhua|luo.zhiyong|luo.zhuhua|luo.zhehui|luo.zhifeng|luo.zhanghua|luo.zhiyuan|luo.zhijiang|luo.zuhua|luo.zhizeng|luo.zhonghui|luo.zhaonan|luo.zongwei|luo.zhensheng|luo.zongjun|luo.zhengxiang|luo.zhehu|luo.zhijian|luo.zhimin|luo.zunli|luo.zhenguo|luo.zhimeng|luo.zhihua|luo.zhixing|luo.zudao|luo.zhiqiang|luo.zhanhai|luo.zhen|luo.zhengqin|luo.zeju|luo.zongdui|luo.zhangjie|luo.zhihong|luo.zhenhuang|luo.zhikun|luo.ziqiang|luo.zijian|luo.zewei|luo.zi-ping|luo.zhaofu|luo.zhengyuan|luo.zhijun|luo.zongyang|luo.zheng|luo.zhaoxia|luo.zhongyang|luo.zhilin|luo.zhaohua|luo.zhangtao|luo.zhenwei"Nie, W. F."https://www.zbmath.org/authors/?q=ai:nie.weifang"Feng, Y. Y."https://www.zbmath.org/authors/?q=ai:feng.yunyun|feng.youyi|feng.youyong|feng.yiying|feng.yuying|feng.yingying|feng.yuyu|feng.yuanyuan|feng.yiyong|feng.yangyue|feng.yuyou|feng.yaoyao|feng.yanyan|feng.yanying"Lan, X. G."https://www.zbmath.org/authors/?q=ai:lan.xiao-gang|lan.xuguangBethe ansatz in stringy sigma models.https://www.zbmath.org/1456.813372021-04-16T16:22:00+00:00"Klose, T."https://www.zbmath.org/authors/?q=ai:klose.thomas"Zarembo, K."https://www.zbmath.org/authors/?q=ai:zarembo.konstantinGravitational positivity bounds.https://www.zbmath.org/1456.830312021-04-16T16:22:00+00:00"Tokuda, Junsei"https://www.zbmath.org/authors/?q=ai:tokuda.junsei"Aoki, Katsuki"https://www.zbmath.org/authors/?q=ai:aoki.katsuki"Hirano, Shin'ichi"https://www.zbmath.org/authors/?q=ai:hirano.shinichiSummary: We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic \(t\)-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with ``wrong'' sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by \({M}_{ \mathrm{pl}}^{-2}\alpha^{\prime}\) where \(\alpha \)' is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.Weights, recursion relations and projective triangulations for positive geometry of scalar theories.https://www.zbmath.org/1456.814542021-04-16T16:22:00+00:00"John, Renjan Rajan"https://www.zbmath.org/authors/?q=ai:john.renjan-rajan"Kojima, Ryota"https://www.zbmath.org/authors/?q=ai:kojima.ryota"Mahato, Sujoy"https://www.zbmath.org/authors/?q=ai:mahato.sujoySummary: The story of positive geometry of massless scalar theories was pioneered in [\textit{N. Arkani-Hamed} et al., J. High Energy Phys. 2018, No. 5, Paper No. 96, 78 p. (2018; Zbl 1391.81200)] in the context of bi-adjoint \(\varphi^3\) theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial interaction is a class of polytopes called accordiohedra. Tree-level planar scattering amplitudes of the theory can be obtained from a weighted sum of the canonical forms of the accordiohedra. In this paper, using results of the recent work [\textit{R. Kojima}, J. High Energy Phys. 2020, No. 8, Paper No. 54, 34 p. (2020; Zbl 1454.81236)], we show that in theories with polynomial interactions all the weights can be determined from the factorization property of the accordiohedron. We also extend the projective recursion relations to these theories. We then give a detailed analysis of how the recursion relations in \(\varphi^p\) theories and theories with polynomial interaction correspond to projective triangulations of accordiohedra. Following recent development we also extend our analysis to one-loop integrands in the quartic theory.Lifting heptagon symbols to functions.https://www.zbmath.org/1456.814282021-04-16T16:22:00+00:00"Dixon, Lance J."https://www.zbmath.org/authors/?q=ai:dixon.lance-j"Liu, Yu-Ting"https://www.zbmath.org/authors/?q=ai:liu.yutingSummary: Seven-point amplitudes in planar \(\mathcal{N} = 4\) super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface. To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six. We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.Landau diagrams in AdS and S-matrices from conformal correlators.https://www.zbmath.org/1456.814552021-04-16T16:22:00+00:00"Komatsu, Shota"https://www.zbmath.org/authors/?q=ai:komatsu.shota"Paulos, Miguel F."https://www.zbmath.org/authors/?q=ai:paulos.miguel-f"van Rees, Balt C."https://www.zbmath.org/authors/?q=ai:van-rees.balt-c"Zhao, Xiang"https://www.zbmath.org/authors/?q=ai:zhao.xiangSummary: Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in [\textit{M. F. Paulos} et al., J. High Energy Phys. 2017, No. 11, Paper No. 133, 45 p. (2017; Zbl 1383.81251)] based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called `bad regions', where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.Quantum-unbinding near a zero temperature liquid-gas transition.https://www.zbmath.org/1456.814502021-04-16T16:22:00+00:00"Zwerger, Wilhelm"https://www.zbmath.org/authors/?q=ai:zwerger.wilhelmFinite-temperature dynamical correlations in massive integrable quantum field theories.https://www.zbmath.org/1456.812312021-04-16T16:22:00+00:00"Essler, Fabian H. L."https://www.zbmath.org/authors/?q=ai:essler.fabian-h-l"Konik, Robert M."https://www.zbmath.org/authors/?q=ai:konik.robert-mExtremal black hole scattering at \(\mathcal{O} (G^3)\): graviton dominance, eikonal exponentiation, and differential equations.https://www.zbmath.org/1456.831172021-04-16T16:22:00+00:00"Parra-Martinez, Julio"https://www.zbmath.org/authors/?q=ai:parra-martinez.julio"Ruf, Michael S."https://www.zbmath.org/authors/?q=ai:ruf.michael-s"Zeng, Mao"https://www.zbmath.org/authors/?q=ai:zeng.maoSummary: We use \(\mathcal{N} = 8\) supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at \(\mathcal{O} (G^3)\) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known \(D\)-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by \textit{Z. Bern} et al. [J. High Energy Phys. 2019, No. 10, Paper No. 206, 135 p. (2019; Zbl 1427.83035)] in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.S matrix for a three-parameter integrable deformation of \( \mathrm{AdS}_3 \times S^3\) strings.https://www.zbmath.org/1456.814512021-04-16T16:22:00+00:00"Bocconcello, Marco"https://www.zbmath.org/authors/?q=ai:bocconcello.marco"Masuda, Isari"https://www.zbmath.org/authors/?q=ai:masuda.isari"Seibold, Fiona K."https://www.zbmath.org/authors/?q=ai:seibold.fiona-k"Sfondrini, Alessandro"https://www.zbmath.org/authors/?q=ai:sfondrini.alessandroSummary: We consider the three-parameter integrable deformation of the \( \mathrm{AdS}_3 \times S^3\) superstring background constructed in [\textit{F. Delduc} et al., J. High Energy Phys. 2019, No. 1, Paper No. 109, 25 p. (2019; Zbl 1414.81129)]. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.Quasilocal charges and progress towards the complete GGE for field theories with nondiagonal scattering.https://www.zbmath.org/1456.814492021-04-16T16:22:00+00:00"Vernier, Eric"https://www.zbmath.org/authors/?q=ai:vernier.eric"Cortés Cubero, Axel"https://www.zbmath.org/authors/?q=ai:cubero.axel-cortesSoft photon theorems from CFT Ward identites in the flat limit of AdS/CFT.https://www.zbmath.org/1456.813832021-04-16T16:22:00+00:00"Hijano, Eliot"https://www.zbmath.org/authors/?q=ai:hijano.eliot"Neuenfeld, Dominik"https://www.zbmath.org/authors/?q=ai:neuenfeld.dominikSummary: S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by taking the flat limit of bulk operator reconstruction techniques. Using this method, we obtain explicit expressions for incoming and outgoing U(1) gauge fields. Weinberg soft photon theorems then follow from Ward identites of conserved CFT currents. In four bulk dimensions, gauge fields on AdS can be quantized with standard and alternative boundary conditions. Changing the quantization scheme corresponds to the \(S\)-transformation of \(\mathrm{SL}(2, \mathbb{Z})\) electric-magnetic duality in the bulk. This allows us to derive both, the electric and magnetic soft photon theorems in flat space from CFT physics.Duality and supersymmetry constraints on the weak gravity conjecture.https://www.zbmath.org/1456.830112021-04-16T16:22:00+00:00"Loges, Gregory J."https://www.zbmath.org/authors/?q=ai:loges.gregory-j"Noumi, Toshifumi"https://www.zbmath.org/authors/?q=ai:noumi.toshifumi"Shiu, Gary"https://www.zbmath.org/authors/?q=ai:shiu.garySummary: Positivity bounds coming from consistency of UV scattering amplitudes are not always sufficient to prove the weak gravity conjecture for theories beyond Einstein-Maxwell. Additional ingredients about the UV may be necessary to exclude those regions of parameter space which are naïvely in conflict with the predictions of the weak gravity conjecture. In this paper we explore the consequences of imposing additional symmetries inherited from the UV theory on higher-derivative operators for Einstein-Maxwell-dilaton-axion theory. Using black hole thermodynamics, for a preserved \( \mathrm{SL}(2, \mathbb{R})\) symmetry we find that the weak gravity conjecture then does follow from positivity bounds. For a preserved \( \mathrm{O}( d, d; \mathbb{R})\) symmetry we find a simple condition on the two Wilson coefficients which ensures the positivity of corrections to the charge-to-mass ratio and that follows from the null energy condition alone. We find that imposing supersymmetry on top of either of these symmetries gives corrections which vanish identically, as expected for BPS states.Frobenius-Perron eigenstates in deformed microdisk cavities: non-Hermitian physics and asymmetric backscattering in ray dynamics.https://www.zbmath.org/1456.814482021-04-16T16:22:00+00:00"Kullig, Julius"https://www.zbmath.org/authors/?q=ai:kullig.julius"Wiersig, Jan"https://www.zbmath.org/authors/?q=ai:wiersig.janS-matrix approach to quantum gases in the unitary limit. I: The two-dimensional case.https://www.zbmath.org/1456.822712021-04-16T16:22:00+00:00"How, Pye-Ton"https://www.zbmath.org/authors/?q=ai:how.pye-ton"LeClair, André"https://www.zbmath.org/authors/?q=ai:leclair.andreIntegrability, non-integrability and confinement.https://www.zbmath.org/1456.812452021-04-16T16:22:00+00:00"Mussardo, G."https://www.zbmath.org/authors/?q=ai:mussardo.guiseppe|mussardo.giuseppeMulti-Regge limit of the two-loop five-point amplitudes in \(\mathcal{N} = 4\) super Yang-Mills and \(\mathcal{N} = 8\) supergravity.https://www.zbmath.org/1456.831122021-04-16T16:22:00+00:00"Caron-Huot, Simon"https://www.zbmath.org/authors/?q=ai:caron-huot.simon"Chicherin, Dmitry"https://www.zbmath.org/authors/?q=ai:chicherin.dmitry"Henn, Johannes"https://www.zbmath.org/authors/?q=ai:henn.johannes-m"Zhang, Yang"https://www.zbmath.org/authors/?q=ai:zhang.yang"Zoia, Simone"https://www.zbmath.org/authors/?q=ai:zoia.simoneSummary: In previous work [\textit{E. D'Hoker} et al.,ibid. 2020, No. 8, Paper No. 135, 80 p. (2020; Zbl 1454.83159); \textit{C. R. Mafra} and \textit{O. Schlotterer}, ibid. 2015, No. 10, Paper No. 124, 29 p. (2015; Zbl 1388.83860)], the two-loop five-point amplitudes in \(\mathcal{N} = 4\) super Yang-Mills theory and \(\mathcal{N} = 8\) supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the \(\mathcal{N} = 4\) super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.Publisher's note: ``Semiclassical WKB problem for the non-self-adjoint Dirac operator with analytic potential'' [J. Math. Phys. 61, 011510 (2020)].https://www.zbmath.org/1456.811832021-04-16T16:22:00+00:00"Fujiié, Setsuro"https://www.zbmath.org/authors/?q=ai:fujiie.setsuro"Kamvissis, Spyridon"https://www.zbmath.org/authors/?q=ai:kamvissis.spyridonFrom the text: This article was originally published online on 27 January 2020 with errors in the body of the article. Grammatical and layout changes have been made throughout the article. AIP Publishing apologizes for these errors. All online versions of the article were corrected on 7 February; the article is correct as it appears in the printed version of the journal.S-matrix approach to quantum gases in the unitary limit. II: The three-dimensional case.https://www.zbmath.org/1456.820472021-04-16T16:22:00+00:00"How, Pye-Ton"https://www.zbmath.org/authors/?q=ai:how.pye-ton"LeClair, André"https://www.zbmath.org/authors/?q=ai:leclair.andreGeneralized planar Feynman diagrams: collections.https://www.zbmath.org/1456.813192021-04-16T16:22:00+00:00"Borges, Francisco"https://www.zbmath.org/authors/?q=ai:borges.francisco"Cachazo, Freddy"https://www.zbmath.org/authors/?q=ai:cachazo.freddySummary: Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each degeneration of a tree leads to a single planar neighbor. Amplitudes are computed as an integral over the space of metrics where edge lengths are Schwinger parameters. In this work we propose that a natural generalization of Feynman diagrams is provided by what are known as metric tree arrangements. These are collections of metric trees subject to a compatibility condition on the metrics. We introduce the notion of \textit{planar col lections of Feynman diagrams} and argue that using planarity one can generate all planar collections starting from any one. Moreover, we identify a canonical initial collection for all \(n\). Generalized \(k = 3\) biadjoint amplitudes, introduced by Early, Guevara, Mizera, and one of the authors, are easily computed as an integral over the space of metrics of planar collections of Feynman diagrams.Gravitational shock waves and scattering amplitudes.https://www.zbmath.org/1456.830132021-04-16T16:22:00+00:00"Cristofoli, Andrea"https://www.zbmath.org/authors/?q=ai:cristofoli.andreaSummary: We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by exploiting a novel relation between scattering amplitudes and solutions to Einstein field equations. We prove that gravitational shock waves arise from the classical part of a three point function with two massless scalars and a graviton. The region where radiation is localized has a distributional profile and it is now recovered in a natural way, thus bypassing the introduction of singular coordinate transformations as used in General Relativity. The computation is easily generalized to arbitrary dimensions and we show how the exactness of the classical solution follows from the absence of classical contributions at higher loops. A classical double copy between gravitational and electromagnetic shock waves is also provided and for a spinning source, using the exponential form of three point amplitudes, we infer a remarkable relation between gravitational shock waves and spinning ones, also known as gyratons. Using this property, we infer a family of exact solutions describing gravitational shock waves with spin. We then compute the phase shift of a particle in a background of shock waves finding agreement with an earlier computation by Amati, Ciafaloni and Veneziano for particles in the high energy limit. Applied to a gyraton, it provides a result for the scattering angle to all orders in spin.Scattering equations in AdS: scalar correlators in arbitrary dimensions.https://www.zbmath.org/1456.830962021-04-16T16:22:00+00:00"Eberhardt, Lorenz"https://www.zbmath.org/authors/?q=ai:eberhardt.lorenz"Komatsu, Shota"https://www.zbmath.org/authors/?q=ai:komatsu.shota"Mizera, Sebastian"https://www.zbmath.org/authors/?q=ai:mizera.sebastianSummary: We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two current algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.The \(sl (2|1)^{(2)}\) Gaudin magnet with diagonal boundary terms.https://www.zbmath.org/1456.822892021-04-16T16:22:00+00:00"Lima-Santos, A."https://www.zbmath.org/authors/?q=ai:lima-santos.antonioA scattering amplitude in conformal field theory.https://www.zbmath.org/1456.813782021-04-16T16:22:00+00:00"Gillioz, Marc"https://www.zbmath.org/authors/?q=ai:gillioz.marc"Meineri, Marco"https://www.zbmath.org/authors/?q=ai:meineri.marco"Penedones, João"https://www.zbmath.org/authors/?q=ai:penedones.joaoSummary: We define form factors and scattering amplitudes in conformal field theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as \(p^2 \rightarrow 0\). In particular, we study a form factor \(F(s, t, u) \) obtained from a four-point function of identical scalar primary operators. We show that \(F\) is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the \textit{3d} Ising model, perturbative fixed points and holographic CFTs.Graviton-mediated scattering amplitudes from the quantum effective action.https://www.zbmath.org/1456.830222021-04-16T16:22:00+00:00"Draper, Tom"https://www.zbmath.org/authors/?q=ai:draper.tom"Knorr, Benjamin"https://www.zbmath.org/authors/?q=ai:knorr.benjamin"Ripken, Chris"https://www.zbmath.org/authors/?q=ai:ripken.chris"Saueressig, Frank"https://www.zbmath.org/authors/?q=ai:saueressig.frankSummary: We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.A Lorentz-covariant interacting electron-photon system in one space dimension.https://www.zbmath.org/1456.812602021-04-16T16:22:00+00:00"Kiessling, Michael K.-H."https://www.zbmath.org/authors/?q=ai:kiessling.michael-karl-heinz"Lienert, Matthias"https://www.zbmath.org/authors/?q=ai:lienert.matthias"Tahvildar-Zadeh, A. Shadi"https://www.zbmath.org/authors/?q=ai:tahvildar-zadeh.a-shadiSummary: A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of multi-time wave functions, i.e., wave functions \(\Psi^{(2)}(\mathbf{x}_{\mathrm{ph}},\mathbf{x}_{\mathrm{el}})\) where \(\mathbf{x}_{\mathrm{el}},\mathbf{x}_{\mathrm{ph}}\) are the generic spacetime events of the electron and photon, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifold \(\{\mathbf{x}_{\mathrm{el}}=\mathbf{x}_{\mathrm{ph}}\} \), compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed. Electron and photon trajectories are shown to exist globally in a hypersurface Bohm-Dirac theory, for typical particle initial conditions. Also presented are the results of some numerical experiments which illustrate Compton scattering as well as a new phenomenon: photon capture and release by the electron.Degenerate band edges in periodic quantum graphs.https://www.zbmath.org/1456.811942021-04-16T16:22:00+00:00"Berkolaiko, Gregory"https://www.zbmath.org/authors/?q=ai:berkolaiko.gregory"Kha, Minh"https://www.zbmath.org/authors/?q=ai:kha.minhSummary: Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet-Bloch transform. It is often assumed that the extrema generating the band edges are non-degenerate. This paper constructs a family of examples of \({\mathbb{Z}}^3\)-periodic quantum graphs where the non-degeneracy assumption fails: the maximum of the first band is achieved along an algebraic curve of co-dimension 2. The example is robust with respect to perturbations of edge lengths, vertex conditions and edge potentials. The simple idea behind the construction allows generalizations to more complicated graphs and lattice dimensions. The curves along which extrema are achieved have a natural interpretation as moduli spaces of planar polygons.Building bases of loop integrands.https://www.zbmath.org/1456.813002021-04-16T16:22:00+00:00"Bourjaily, Jacob L."https://www.zbmath.org/authors/?q=ai:bourjaily.jacob-l"Herrmann, Enrico"https://www.zbmath.org/authors/?q=ai:herrmann.enrico"Langer, Cameron"https://www.zbmath.org/authors/?q=ai:langer.cameron-k"Trnka, Jaroslav"https://www.zbmath.org/authors/?q=ai:trnka.jaroslavSummary: We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting' for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all `leading-(transcendental-)weight' contributions of \textit{any} four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent \textit{all} scattering amplitude integrands in the theory --- for generic helicities and arbitrary multiplicity.Dual S-matrix bootstrap. Part I. 2D theory.https://www.zbmath.org/1456.814532021-04-16T16:22:00+00:00"Guerrieri, Andrea L."https://www.zbmath.org/authors/?q=ai:guerrieri.andrea-l"Homrich, Alexandre"https://www.zbmath.org/authors/?q=ai:homrich.alexandre"Vieira, Pedro"https://www.zbmath.org/authors/?q=ai:vieira.pedro-sampaio|vieira.pedro-gSummary: Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.Propagators, BCFW recursion and new scattering equations at one loop.https://www.zbmath.org/1456.814522021-04-16T16:22:00+00:00"Farrow, Joseph A."https://www.zbmath.org/authors/?q=ai:farrow.joseph-a"Geyer, Yvonne"https://www.zbmath.org/authors/?q=ai:geyer.yvonne"Lipstein, Arthur E."https://www.zbmath.org/authors/?q=ai:lipstein.arthur-e"Monteiro, Ricardo"https://www.zbmath.org/authors/?q=ai:monteiro.ricardo"Stark-Muchão, Ricardo"https://www.zbmath.org/authors/?q=ai:stark-muchao.ricardoSummary: We investigate how loop-level propagators arise from tree level via a forward-limit procedure in two modern approaches to scattering amplitudes, namely the BCFW recursion relations and the scattering equations formalism. In the first part of the paper, we revisit the BCFW construction of one-loop integrands in momentum space, using a convenient parametrisation of the \(D\)-dimensional loop momentum. We work out explicit examples with and without supersymmetry, and discuss the non-planar case in both gauge theory and gravity. In the second part of the paper, we study an alternative approach to one-loop integrands, where these are written as worldsheet formulas based on new one-loop scattering equations. These equations, which are inspired by BCFW, lead to standard Feynman-type propagators, instead of the `linear'-type loop-level propagators that first arose from the formalism of ambitwistor strings. We exploit the analogies between the two approaches, and present a proof of an all-multiplicity worldsheet formula using the BCFW recursion.