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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-08-01 DOI: 10.1063/5.0196609
Renata Ferrero, Markus B. Fröb, William C. C. Lima
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.
我们计算了大质量引力正则化和重正则化所需的热核系数。从大质量引力的斯图科尔伯格作用出发,我们确定了不同场(大质量张量、矢量和标量)在一般线性协变规中的传播者,这取决于四个自由规参数。然后,我们计算标量、矢量和张量部门所有分量的非最小热核系数,并利用这些系数正则化大质量引力所有不同场的传播者。我们还研究了无质量极限,并讨论了范达姆-韦尔曼-扎哈罗夫不连续性的出现。在计算过程中,我们得出了与不同场扇区(包括大质量和无质量)的热核系数相关的新等式。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-08-01 DOI: 10.1063/5.0218349
Samuel O. Scalet
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.
我们考虑的问题是逼近具有有限范围的平移不变一维量子自旋系统的自由能密度。由于与已知硬度结果的问题密切相关,这个问题的复杂性并不复杂,但最近有人提出了一种经典的亚对数时间算法[Fawzi 等人,2022]。结合之前用于相关问题的几种算法技术,我们提出了一种渐近优于这一结果的算法,并给出了严格的运行时间界限。我们的主要技术是使用相变不存在结果中已知的荒木扩展和矩阵积算子构造。我们还回顾了一种使用量子信念传播的相关方法[Kuwahara et al., 2018],结合我们的发现,可以得到等效的结果。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-25 DOI: 10.1063/5.0194370
Khalid Ahbli, Fouzia El Wassouli, Zouhaïr Mouayn
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.
在讨论一类广义复赫米特多项式时,我们讨论了它们的一些基本性质,并给出了伯克纳尔式的运算公式。我们还推导出新的结果,包括尼尔森特性、生成函数和 Runge 加法公式。这些多项式还可用于定义谐振子的一组非线性相干态。它们也可被视为朗道型算子的特征函数。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-25 DOI: 10.1063/5.0180748
Changlin Liu, Ying Lv, Zengqi Ou
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.
本文研究了非线性基尔霍夫型方程-a+b∫RN|∇u|2dxΔu=λu+|u|p-2u+|u|q-2u在RN中的归一化解的非存在性和存在性,其中N = 1, 2, 3, a, b &;gt; 0 为常数,q=2+8N 为基尔霍夫方程的 L2 临界指数,p=2+4N 为 "局部 "方程的 L2 临界指数。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-25 DOI: 10.1063/5.0159643
Gabor Toth
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.
我们分析了二元舆论动态的伽拉姆模型的一个广义模型,在该模型中,迭代讨论是在由个人组成的局部群体中进行的,并研究了随机偏离群体多数的影响。偏离或翻转的概率取决于多数的大小。翻转参数决定了偏离的概率,根据翻转参数值的不同,模型会表现出各种各样的行为。我们感兴趣的是当翻转参数本身是按照某种概率分布随机选择时,模型的特征。这些特征的例子包括大多数和平局是吸引还是排斥,或者模型动态中的固定点数量。模型的哪些特征可能出现?哪些是不可能出现的,因为相对于翻转参数的分布,它们只是作为低概率事件出现?回答了这些问题,我们就能将在各种翻转参数分布假设条件下都很稳定的数学特性与非常罕见、因此理论意义大于实际意义的特性区分开来。在本文中,我们既给出了翻转参数特定分布和小型讨论组的精确数值结果,也给出了大型讨论组的极限定理形式的严谨结果。小型讨论组是朋友或工作小组的模型--人们彼此认识并经常在一起。大型讨论组代表社交媒体等场景或城市、州或国家等政治实体。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1063/5.0202635
Pasquale Marra, Valerio Proietti, Xiaobing Sheng
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.
霍夫斯塔德模型可以描述和理解凝聚态物质中的一些现象,如量子霍尔效应、安德森局域化、电荷泵浦和准周期结构中的平带,是量子世界中分形的一个罕见例子。相对论户田晶格是一个看似毫不相干的系统,但在复杂非线性动力学的背景下已被广泛研究,最近又因其与高能物理中 Calabi-Yau 流形上的超对称杨-米尔斯理论和拓扑弦理论的联系而被广泛研究。在此,我们讨论最近发现的霍夫斯塔德模型与相对论户田晶格之间的谱关系,这种谱关系后来被猜测与量子群的朗兰兹对偶性有关。此外,通过采用与量子群结构兼容的相似变换,我们建立了一个公式,用基本对称多项式和切比雪夫多项式参数化了霍夫斯塔德模型的能谱。使用的主要工具是三对角矩阵的谱对偶性和基本量子群的表示理论。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1063/5.0203079
D. D. McNutt, R. J. van den Hoogen, A. A. Coley
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.
对称框架形式主义是计算黎曼-卡尔坦几何对称性的有效工具,特别是在度量远平行几何中。在四维黎曼-卡尔坦几何中扭转不相等的情况下,闵科夫斯基几何是唯一允许十个仿射框架对称的几何。除去这个几何,仿射框架对称的最大数目是七个。一个自然而然的问题是,有哪些四维几何包含七维仿射框架对称群。这样的几何图形是局部均质的,并且允许最大的各向同性群,因此被称为最大各向同性几何图形。利用对称框形式主义计算仿射框对称性以及扭转张量的附加结构,我们采用 Cartan-Karlhede 算法来确定黎曼-卡尔坦几何的所有可能的七维对称群。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-24 DOI: 10.1063/5.0150027
Savan Hirpara, Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço Costa
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.
1977年,吕舍尔在闵科夫斯基空间发现了一类SO(4)-对称SU(2)杨-米尔斯解,40年后,通过使用等距S3 ≅ SU(2)和共形映射杨-米尔斯方程在(两份)德西特空间dS4≅R×S3上的SU(2)-后向解,这些解被重新推导出来。在这里,我们通过 AdS3 ≅ SU(1, 1) 来介绍这一构造的非紧凑类似物。在(两份)反德西特空间 AdS4≅R×AdS3 上,我们写下 SU(1,1)-Quivariant Yang-Mills 解,并将它们保角映射到 R1,3。这样就得到了闵科夫斯基空间上精确的 SU(1,1) 杨-米尔斯解的双参数族,其场强本质上是笛卡尔坐标的有理函数。两个 AdS 副本的粘合发生在闵科夫斯基空间的 dS3 双曲面上,我们的杨-米尔斯构型在二维双曲面 dS3∩R1,2 上是奇异的。这使得它们的作用和能量都是无限的,尽管除了沿着光锥之外,场强都会快速地渐近下降。我们还构造了阿贝尔解,它们也具有这些性质,但对称性较差,作用为零。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1063/5.0209344
Armando J. Cabrera Pacheco, Markus Wolff
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.
受 Rácz 于 2016 年提出的以演化形式求解约束方程的启发,我们提出了一个近似平坦的初始数据集系列,这些数据集在无穷远处 "近似球面对称"。在这个族中,我们得到了类似彭罗斯的能量估计,并确定了约束方程在球对称和全脐情况下的解的存在性。
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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 Q3 PHYSICS, MATHEMATICAL Pub Date : 2024-07-23 DOI: 10.1063/5.0196379
Santanu Tantubay, Priyanshu Chakraborty
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.
环形李代数是仿射 Kac-Moody 李代数的 n 变广义。全环形李代数是环形李代数和维特代数的派生李代数的半间接积,也可以认为是仿射-维拉索罗代数的 n 变广义。设 h̃ 是环形李代数的 Cartan 子代数,也是不含零度中心元的全环形李代数。在本文中,我们将 U(h̃) 上的模块结构分类为所有环形李代数和全环形李代数,它们都是秩为 1 的自由 U(h̃)- 模块。这些模块只存在于 Al(l ≥ 1), Cl(l ≥ 2) 型环形李代数中,对于全环形李代数也是如此。此外,我们还确定了这两个列阵的这些类模块的不可还原性条件。
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引用次数: 0
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Journal of Mathematical Physics
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