Recent zbMATH articles in MSC 81T20https://www.zbmath.org/atom/cc/81T202021-04-16T16:22:00+00:00WerkzeugSemi-classical limit of quantum free energy minimizers for the gravitational Hartree equation.https://www.zbmath.org/1456.811882021-04-16T16:22:00+00:00"Choi, Woocheol"https://www.zbmath.org/authors/?q=ai:choi.woocheol"Hong, Younghun"https://www.zbmath.org/authors/?q=ai:hong.younghun"Seok, Jinmyoung"https://www.zbmath.org/authors/?q=ai:seok.jinmyoungThe authors consider the gravitational Vlasov-Poisson equation for a plasma in a gravitational field. They assume that their approach would be valid for large complexes of stars like white dwarfs with a number of stars $N>10^8$ or $N>10^{14}$ for giant stars. The main idea of the actual article is as follows. There is a number of research in which one construct free energy minimizers under some mass constrains.
From an another hand there are also researches which investigate free energy minimizers for the quantum problem, based on the well known Hartree-Fock mean field method.
The problem which is solved by the authors of the actual article concerns with the correspondence between quantum and classical isotropic states. The authors prove some theorems stating that in the limit of very small quantum Planck constant ( when the Planck constant is going to 0), the free energy minimizers for the Hartree-Fock equation converge to those for the Vlasov-Poisson equation in terms of potential functions, as well as via the Wigner transform and the Toplitz quantization.
The authors mention throughout the text of the article an earlier research (1961, 1962) by V.A. Antonov, which is proving the stability of the Vlasov-Poisson equation, applied for stellar many-bodies systems with large number of components. Let us mention, that the famous paper by A.A. Vlasov which established a new kinetic equation for plasma was published in 1938 and only much later was recognized as a correct equation for plasma. See, about this the book by \textit{I. P. Bazarov}, and \textit{P. N. Nikolaev} [Anatolij Aleksandrovich Vlasov ( in Russian), 2nd edition, 63 p. (1999; \url{http:// phys.msu.ru/upload/iblock/0cc/ vlasov-book.pdf})].
Reviewer: Alex B. Gaina (Chisinau)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.Topological field theories of 2- and 3-forms in six dimensions.https://www.zbmath.org/1456.814072021-04-16T16:22:00+00:00"Herfray, Yannick"https://www.zbmath.org/authors/?q=ai:herfray.yannick"Krasnov, Kirill"https://www.zbmath.org/authors/?q=ai:krasnov.kirill-vSummary: We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term \(BdC\) but differ in the potential term that is added. The theory \(BdC\) with no potential term is topological -- it describes no propagating degrees of freedom. We show that the theory continues to remain topological when either the \(BBB\) or \(C \hat{C}\) potential term is added. The latter theory can be viewed as a background independent version of the 6-dimensional Hitchin theory, for its critical points are complex or para-complex 6-manifolds, but unlike in Hitchin's construction, one does not need to choose a background cohomology class to define the theory. We also show that the dimensional reduction of the \(C \hat{C}\) theory to three dimensions, when reducing on \(S^{3}\), gives 3D gravity.{
\copyright 2017 American Institute of Physics}Aharonov-Bohm superselection sectors.https://www.zbmath.org/1456.812972021-04-16T16:22:00+00:00"Dappiaggi, Claudio"https://www.zbmath.org/authors/?q=ai:dappiaggi.claudio"Ruzzi, Giuseppe"https://www.zbmath.org/authors/?q=ai:ruzzi.giuseppe"Vasselli, Ezio"https://www.zbmath.org/authors/?q=ai:vasselli.ezioSummary: We show that the Aharonov-Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper, we show that this ``topological'' quantum number amounts to the presence of a background flat potential which rules the behaviour of charges when transported along paths as in the Aharonov-Bohm effect. To confirm these abstract results, we quantize the Dirac field in the presence of a background flat potential and show that the Aharonov-Bohm phase gives an irreducible representation of the fundamental group of the spacetime labelling the charged sectors of the Dirac field. We also show that non-abelian generalizations of this effect are possible only on spacetimes with a non-abelian fundamental group.Multi-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.