Reviews in Mathematical Physics最新文献

{"title":"Painleve equations, integrable systems and the stabilizer set of Virasoro orbit","authors":"J. Cariñena, P. Guha, M. F. Ranada","doi":"10.1142/s0129055x23300042","DOIUrl":"https://doi.org/10.1142/s0129055x23300042","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47127972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Framed 𝔼n-algebras from quantum field theory","authors":"C. Elliott, Owen Gwilliam","doi":"10.1142/s0129055x23500113","DOIUrl":"https://doi.org/10.1142/s0129055x23500113","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42377977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a new proof of the Okuyama–Sakai conjecture","authors":"Di Yang, Qingsheng Zhang","doi":"10.1142/s0129055x23500253","DOIUrl":"https://doi.org/10.1142/s0129055x23500253","url":null,"abstract":"Okuyama and Sakai [JT supergravity and Brézin–Gross–Witten tau-function, J. High Energy Phys. 2020 (2020) 160] gave a conjectural equality for the higher genus generalized Brézin–Gross–Witten (BGW) free energies. In a recent work [D. Yang and Q. Zhang, On the Hodge-BGW correspondence, preprint (2021), arXiv:2112.12736], we established the Hodge-BGW correspondence on the relationship between certain special cubic Hodge integrals and the generalized BGW correlators, and a proof of the Okuyama–Sakai conjecture was also given ibid. In this paper, we give a new proof of the Okuyama–Sakai conjecture by a further application of the Dubrovin–Zhang theory for the KdV hierarchy.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"24 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64122010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-free states on a class of algebras of multicomponent commutation relations","authors":"E. Lytvynov, Nedal Othman","doi":"10.1142/S0129055X23500204","DOIUrl":"https://doi.org/10.1142/S0129055X23500204","url":null,"abstract":"Multicomponent commutations relations (MCR) describe plektons, i.e., multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix $Q(x_1,x_2)$ that depends on the position of quasiparticles. For such an exchange to be possible, the matrix must satisfy several conditions, including the functional Yang--Baxter equation. The aim of the paper is to give an appropriate definition of a quasi-free state on an MCR algebra, and construct such states on a class of MCR algebras. We observe a significant difference between the classical setting for bosons and fermions and the setting of MCR algebras. We show that the developed theory is applicable to systems that contain quasiparticles of opposite type. An example of such a system is a two-component system in which two quasiparticles, under exchange, change their respective types to the opposite ones ($1mapsto 2$, $2mapsto1$). Fusion of quasiparticles means intuitively putting several quasiparticles in an infinitely small box and identifying the statistical behaviour of the box. By carrying out fusion of an odd number of particles from the two-component system as described above, we obtain further examples of quantum systems to which the developed theory is applicable.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48045594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetries in non-relativistic quantum electrodynamics","authors":"D. Hasler, Markus Lange","doi":"10.1142/S0129055X23500186","DOIUrl":"https://doi.org/10.1142/S0129055X23500186","url":null,"abstract":"We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space representation as well as in the Schr\"odinger representation. As an application, we generalize and improve theorems about Kramer's degeneracy in non-relativistic quantum electrodynamics.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42999987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Canonical BV Laplacian on Half-Densities","authors":"A. Cattaneo","doi":"10.1142/S0129055X23300030","DOIUrl":"https://doi.org/10.1142/S0129055X23300030","url":null,"abstract":"This is a didactical review on the canonical BV Laplacian on half-densities.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45227645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On thermodynamic and ultraviolet stability bounds for bosonic lattice QCD models in Euclidean dimensions d = 2,3,4","authors":"P. A. F. da Veiga, M. O'carroll","doi":"10.1142/s0129055x23500046","DOIUrl":"https://doi.org/10.1142/s0129055x23500046","url":null,"abstract":"We prove thermodynamic and ultraviolet stable stability bounds for lattice scalar QCD quantum models, with multiflavor real or complex scalar Bose matter fields and a compact, connected gauge Lie group [Formula: see text], [Formula: see text] with Lie algebra dimension [Formula: see text]. Our models are defined on a finite hypercubic lattice [Formula: see text], [Formula: see text], [Formula: see text], with [Formula: see text], even, sites on a side, [Formula: see text] sites, and with free boundary conditions. The models action is a sum of a minimally coupled Bose-gauge part and a Wilson pure-gauge plaquette action. We use local, scaled scalar multiflavor Bose fields. The scaling is global, [Formula: see text]-dependent and noncanonical, and corresponds to an a priori renormalization. The Wilson action is a sum over positive plaquette actions times a factor [Formula: see text], with the gauge coupling [Formula: see text] in [Formula: see text], [Formula: see text]. By local gauge invariance, to eliminate the excess of gauge variables, sometimes we use an enhanced temporal gauge, leaving only [Formula: see text] for [Formula: see text], retained bonds. Fixing this gauge does not alter the value of the partition function. Considering the original physical, unscaled partition function [Formula: see text], where [Formula: see text] is the unscaled (bare) hopping parameter and [Formula: see text] are the boson fields bare masses, and letting [Formula: see text] and [Formula: see text], we show that the scaled partition function [Formula: see text] satisfies the thermodynamic and ultraviolet stable stability bounds [Formula: see text], with finite constants [Formula: see text], independent of the lattice size [Formula: see text] of [Formula: see text] and the spacing [Formula: see text]. For the normalized finite-lattice free energy [Formula: see text], a finite thermodynamic limit ([Formula: see text]) for [Formula: see text], and then the continuum limit [Formula: see text], both exist in the sense of subsequences. They give the model normalized free energies [Formula: see text]. The finiteness of [Formula: see text] is the only question addressed here! The use of the Weyl integration formula is essential in showing these bounds. It allows us to replace the gauge integral over [Formula: see text] gauge bond matrix elements by the integration over its [Formula: see text] eigenvalues. A new global upper bound on the Wilson plaquette action is obtained, which is quadratic in the gluon fields. Our method bypasses the use of diamagnetic inequality and can be extended to treat more general lattices and Lie gauge groups.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46228578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Araki's extension of the Jordan-Wigner transformation","authors":"W. Aschbacher","doi":"10.1142/S0129055X23300017","DOIUrl":"https://doi.org/10.1142/S0129055X23300017","url":null,"abstract":"In his seminal paper [1], Araki introduced an elegant extension of the Jordan-Wigner transformation which establishes a precise connection between quantum spin systems and Fermi lattice gases in one dimension in the so-called infinite system idealization of quantum statistical mechanics. His extension allows in particular for the rigorous study of numerous aspects of the prominent XY chain over the two sided infinite discrete line without having to resort to a thermodynamic limit procedure at an intermediate or at the final stage. We rigorously review and elaborate this extension from scratch which makes the paper rather self-contained. In the course of the construction, we also present a simple and concrete realization of Araki’s crossed product extension. Mathematics Subject Classifications (2010) 16S35, 46L55, 47L90, 82B10, 82B23, 82C10.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41714013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Feynman checkers: number-theoretic properties","authors":"Fedor Kuyanov, Alexey Slizkov","doi":"10.1142/s0129055x23500228","DOIUrl":"https://doi.org/10.1142/s0129055x23500228","url":null,"abstract":"We study Feynman checkers, an elementary model of electron motion introduced by R. Feynman. In this model, a checker moves on a checkerboard, and we count the turns. Feynman checkers are also known as a one-dimensional quantum walk. We prove some new number-theoretic results in this model, for example, sign alternation of the real and imaginary parts of the electron wave function in a specific area. All our results can be stated in terms of Young diagrams, namely, we compare the number of Young diagrams with an odd and an even number of steps.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49130022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Answer to M. Ben-Artzy, and T. Umeda, Spectral theory of first-order systems: from crystals to Dirac operators, Rev. Math. Phys., 33 5, (2021) 2150014","authors":"R. Weder","doi":"10.1142/s0129055x23500022","DOIUrl":"https://doi.org/10.1142/s0129055x23500022","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45249630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}