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Heat kernel coefficients for massive gravity 大质量重力的热核系数
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1063/5.0196609
Renata Ferrero, Markus B. Fröb, William C. C. Lima
{"title":"Heat kernel coefficients for massive gravity","authors":"Renata Ferrero, Markus B. Fröb, William C. C. Lima","doi":"10.1063/5.0196609","DOIUrl":"https://doi.org/10.1063/5.0196609","url":null,"abstract":"We compute the heat kernel coefficients that are needed for the regularization and renormalization of massive gravity. Starting from the Stueckelberg action for massive gravity, we determine the propagators of the different fields (massive tensor, vector and scalar) in a general linear covariant gauge depending on four free gauge parameters. We then compute the non-minimal heat kernel coefficients for all the components of the scalar, vector and tensor sector, and employ these coefficients to regularize the propagators of all the different fields of massive gravity. We also study the massless limit and discuss the appearance of the van Dam–Veltman–Zakharov discontinuity. In the course of the computation, we derive new identities relating the heat kernel coefficients of different field sectors, both massive and massless.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886296","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}
引用次数: 0
A faster algorithm for the free energy in one-dimensional quantum systems 一维量子系统自由能的快速算法
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-01 DOI: 10.1063/5.0218349
Samuel O. Scalet
{"title":"A faster algorithm for the free energy in one-dimensional quantum systems","authors":"Samuel O. Scalet","doi":"10.1063/5.0218349","DOIUrl":"https://doi.org/10.1063/5.0218349","url":null,"abstract":"We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed [Fawzi et al., 2022]. Combining several algorithmic techniques previously used for related problems, we propose an algorithm outperforming this result asymptotically and give rigorous bounds on its runtime. Our main techniques are the use of Araki expansionals, known from results on the nonexistence of phase transitions, and a matrix product operator construction. We also review a related approach using the Quantum Belief Propagation [Kuwahara et al., 2018], which in combination with our findings yields an equivalent result.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886298","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}
引用次数: 0
Generalized complex Hermite polynomials with associated nonlinear coherent states 具有相关非线性相干态的广义复赫米特多项式
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-25 DOI: 10.1063/5.0194370
Khalid Ahbli, Fouzia El Wassouli, Zouhaïr Mouayn
{"title":"Generalized complex Hermite polynomials with associated nonlinear coherent states","authors":"Khalid Ahbli, Fouzia El Wassouli, Zouhaïr Mouayn","doi":"10.1063/5.0194370","DOIUrl":"https://doi.org/10.1063/5.0194370","url":null,"abstract":"While dealing with a class of generalized complex Hermite polynomials, we discuss some of their basic properties and we give operational formulae of Burchnall-type. New results, including a Nielsen identity, a generating function and a Runge addition formula are derived. These polynomials may also be used to define a set of nonlinear coherent states for the harmonic oscillator. They may also be viewed as eigenfunctions of a Landau-type operator.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770886","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}
引用次数: 0
Normalized solutions for Kirchhoff equation with L2-critical exponents 具有 L2 临界指数的基尔霍夫方程的归一化解
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-25 DOI: 10.1063/5.0180748
Changlin Liu, Ying Lv, Zengqi Ou
{"title":"Normalized solutions for Kirchhoff equation with L2-critical exponents","authors":"Changlin Liu, Ying Lv, Zengqi Ou","doi":"10.1063/5.0180748","DOIUrl":"https://doi.org/10.1063/5.0180748","url":null,"abstract":"In this paper, we study the nonexistence and existence of normalized solutions for the nonlinear Kirchhoff-type equation −a+b∫RN|∇u|2dxΔu=λu+|u|p−2u+|u|q−2u in RN with prescribed L2-norm, where N = 1, 2, 3, a, b > 0 are constants, q=2+8N is L2-critical exponent to Kirchhoff-type Equation, and p=2+4N is the L2-critical exponent to the “local” equation.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770888","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}
引用次数: 0
Models of opinion dynamics with random parametrisation 具有随机参数的舆论动态模型
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-25 DOI: 10.1063/5.0159643
Gabor Toth
{"title":"Models of opinion dynamics with random parametrisation","authors":"Gabor Toth","doi":"10.1063/5.0159643","DOIUrl":"https://doi.org/10.1063/5.0159643","url":null,"abstract":"We analyse a generalisation of the Galam model of binary opinion dynamics in which iterative discussions take place in local groups of individuals and study the effects of random deviations from the group majority. The probability of a deviation or flip depends on the magnitude of the majority. Depending on the values of the flip parameters which give the probability of a deviation, the model shows a wide variety of behaviour. We are interested in the characteristics of the model when the flip parameters are themselves randomly selected, following some probability distribution. Examples of these characteristics are whether large majorities and ties are attractors or repulsors, or the number of fixed points in the dynamics of the model. Which of the features of the model are likely to appear? Which ones are unlikely because they only present as events of low probability with respect to the distribution of the flip parameters? Answers to such questions allow us to distinguish mathematical properties which are stable under a variety of assumptions on the distribution of the flip parameters from features which are very rare and thus more of theoretical than practical interest. In this article, we present both exact numerical results for specific distributions of the flip parameters and small discussion groups and rigorous results in the form of limit theorems for large discussion groups. Small discussion groups model friend or work groups – people that personally know each other and frequently spend time together. Large groups represent scenarios such as social media or political entities such as cities, states, or countries.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770887","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}
引用次数: 0
Hofstadter-Toda spectral duality and quantum groups 霍夫斯塔特-托达谱对偶性与量子群
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-24 DOI: 10.1063/5.0202635
Pasquale Marra, Valerio Proietti, Xiaobing Sheng
{"title":"Hofstadter-Toda spectral duality and quantum groups","authors":"Pasquale Marra, Valerio Proietti, Xiaobing Sheng","doi":"10.1063/5.0202635","DOIUrl":"https://doi.org/10.1063/5.0202635","url":null,"abstract":"The Hofstadter model allows to describe and understand several phenomena in condensed matter such as the quantum Hall effect, Anderson localization, charge pumping, and flat-bands in quasiperiodic structures, and is a rare example of fractality in the quantum world. An apparently unrelated system, the relativistic Toda lattice, has been extensively studied in the context of complex nonlinear dynamics, and more recently for its connection to supersymmetric Yang-Mills theories and topological string theories on Calabi-Yau manifolds in high-energy physics. Here we discuss a recently discovered spectral relationship between the Hofstadter model and the relativistic Toda lattice which has been later conjectured to be related to the Langlands duality of quantum groups. Moreover, by employing similarity transformations compatible with the quantum group structure, we establish a formula parametrizing the energy spectrum of the Hofstadter model in terms of elementary symmetric polynomials and Chebyshev polynomials. The main tools used are the spectral duality of tridiagonal matrices and the representation theory of the elementary quantum group.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770890","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}
引用次数: 0
Locally-homogeneous Riemann-Cartan geometries with the largest symmetry group 具有最大对称群的局部均质黎曼-卡尔坦几何图形
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-24 DOI: 10.1063/5.0203079
D. D. McNutt, R. J. van den Hoogen, A. A. Coley
{"title":"Locally-homogeneous Riemann-Cartan geometries with the largest symmetry group","authors":"D. D. McNutt, R. J. van den Hoogen, A. A. Coley","doi":"10.1063/5.0203079","DOIUrl":"https://doi.org/10.1063/5.0203079","url":null,"abstract":"The symmetry frame formalism is an effective tool for computing the symmetries of a Riemann-Cartan geometry and, in particular, in metric teleparallel geometries. In the case of non-vanishing torsion in a four dimensional Riemann-Cartan geometry, the Minkowski geometry is the only geometry admitting ten affine frame symmetries. Excluding this geometry, the maximal number of affine frame symmetries is seven. A natural question is to ask what four dimensional geometries admit a seven-dimensional group of affine frame symmetries. Such geometries are locally homogeneous and admit the largest isotropy group permitted, and hence are called maximally isotropic. Using the symmetry frame formalism to compute affine frame symmetries along with the additional structure of the torsion tensor, we employ the Cartan-Karlhede algorithm to determine all possible seven-dimensional symmetry groups for Riemann-Cartan geometries.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770893","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}
引用次数: 0
Exact gauge fields from anti-de Sitter space 反德西特空间的精确规量场
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-24 DOI: 10.1063/5.0150027
Savan Hirpara, Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço Costa
{"title":"Exact gauge fields from anti-de Sitter space","authors":"Savan Hirpara, Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço Costa","doi":"10.1063/5.0150027","DOIUrl":"https://doi.org/10.1063/5.0150027","url":null,"abstract":"In 1977 Lüscher found a class of SO(4)-symmetric SU(2) Yang–Mills solutions in Minkowski space, which have been rederived 40 years later by employing the isometry S3 ≅ SU(2) and conformally mapping SU(2)-equivariant solutions of the Yang–Mills equations on (two copies of) de Sitter space dS4≅R×S3. Here we present the noncompact analog of this construction via AdS3 ≅ SU(1, 1). On (two copies of) anti-de Sitter space AdS4≅R×AdS3 we write down SU(1,1)-equivariant Yang–Mills solutions and conformally map them to R1,3. This yields a two-parameter family of exact SU(1,1) Yang–Mills solutions on Minkowski space, whose field strengths are essentially rational functions of Cartesian coordinates. Gluing the two AdS copies happens on a dS3 hyperboloid in Minkowski space, and our Yang–Mills configurations are singular on a two-dimensional hyperboloid dS3∩R1,2. This renders their action and the energy infinite, although the field strengths fall off fast asymptotically except along the lightcone. We also construct Abelian solutions, which share these properties but are less symmetric and of zero action.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770892","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}
引用次数: 0
Families of non time-symmetric initial data sets and Penrose-like energy inequalities 非时间对称初始数据集族和彭罗斯类能量不等式
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-23 DOI: 10.1063/5.0209344
Armando J. Cabrera Pacheco, Markus Wolff
{"title":"Families of non time-symmetric initial data sets and Penrose-like energy inequalities","authors":"Armando J. Cabrera Pacheco, Markus Wolff","doi":"10.1063/5.0209344","DOIUrl":"https://doi.org/10.1063/5.0209344","url":null,"abstract":"Motivated by solving the constraint equations in the evolutionary form suggested by Rácz in 2016, we propose a family of asymptotically flat initial data sets which are “asymptotically spherically symmetric” at infinity. Within this family, we obtain Penrose-like energy estimates and establish the existence of solutions for the constraint equations in the spherical symmetric and totally umbilic cases.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770894","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}
引用次数: 0
Representations of toroidal and full toroidal Lie algebras over polynomial algebras 多项式代数上的环形和全环形李代数的表征
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-23 DOI: 10.1063/5.0196379
Santanu Tantubay, Priyanshu Chakraborty
{"title":"Representations of toroidal and full toroidal Lie algebras over polynomial algebras","authors":"Santanu Tantubay, Priyanshu Chakraborty","doi":"10.1063/5.0196379","DOIUrl":"https://doi.org/10.1063/5.0196379","url":null,"abstract":"Toroidal Lie algebras are n variable generalizations of affine Kac-Moody Lie algebras. Full toroidal Lie algebra is the semidirect product of derived Lie algebra of toroidal Lie algebra and Witt algebra, also it can be thought of n-variable generalization of Affine-Virasoro algebras. Let h̃ be a Cartan subalgebra of a toroidal Lie algebra as well as full toroidal Lie algebra without containing the zero-degree central elements. In this paper, we classify the module structure on U(h̃) for all toroidal Lie algebras as well as full toroidal Lie algebras which are free U(h̃)-modules of rank 1. These modules exist only for type Al(l ≥ 1), Cl(l ≥ 2) toroidal Lie algebras and the same is true for full toroidal Lie algebras. Also, we determined the irreducibility condition for these classes of modules for both the Lie algebras.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770895","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}
引用次数: 0
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