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Criteria for the Absolutely Continuous Spectral Components of matrix-valued Jacobi operators 矩阵值Jacobi算子绝对连续谱分量的判据
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-08-27 DOI: 10.1142/s0129055x22500374
Fabricio Oliveira, Silas Luiz de Carvalho
{"title":"Criteria for the Absolutely Continuous Spectral Components of matrix-valued Jacobi operators","authors":"Fabricio Oliveira, Silas Luiz de Carvalho","doi":"10.1142/s0129055x22500374","DOIUrl":"https://doi.org/10.1142/s0129055x22500374","url":null,"abstract":"We extend in this work the Jitomirskaya-Last inequality and Last-Simoncriterion for the absolutely continuous spectral component of a half-line Schr\"odinger operator to the special class of matrix-valued Jacobi operators $H:l^2(mathbb{Z},mathbb{C})rightarrow l^2(mathbb{Z},mathbb{C})$ given by the law $[H textbf{u}]_{n} := D_{n - 1} textbf{u}_{n - 1} + D_{n} textbf{u}_{n + 1} + V_{n} textbf{u}_{n}$, where $(D_n)_n$ and $(V_n)_n$ are bilateral sequences of $ltimes l$ self-adjoint matrices such that $0<inf_{ninmathbb{Z}}s_l[D_n]lesup_{ninmathbb{Z}}s_1[D_n]<infty$ (here, $s_k[A]$ stands for the $k$-th singular value of $A$). Moreover, we also show that the absolutely continuous components of even multiplicity of minimal dynamically defined matrix-valued Jacobi operators are constant, extending another result from Last-Simon originally proven for scalar Schr\"odinger operators.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44809309","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: 3
Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry 有界几何洛伦兹流形上量子化狄拉克场的哈达玛态
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-08-26 DOI: 10.1142/S0129055X22500088
C. G'erard, Th'eo Stoskopf
{"title":"Hadamard states for quantized Dirac fields on Lorentzian manifolds of bounded geometry","authors":"C. G'erard, Th'eo Stoskopf","doi":"10.1142/S0129055X22500088","DOIUrl":"https://doi.org/10.1142/S0129055X22500088","url":null,"abstract":"We consider Dirac equations on even-dimensional Lorentzian manifolds of bounded geometry with a spin structure. For the associated free quantum field theory, we construct pure Hadamard states using global pseudodifferential calculus on a Cauchy surface. We also give two constructions of Hadamard states for Dirac fields for arbitrary spacetimes with a spin structure.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42660640","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: 7
Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincare group 复化庞加莱群的普遍覆盖的不可约酉表示的回顾和具体描述
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-08-24 DOI: 10.1142/s0129055x22300047
Luigi M. Borasi
{"title":"Review and concrete description of the irreducible unitary representations of the universal cover of the complexified Poincare group","authors":"Luigi M. Borasi","doi":"10.1142/s0129055x22300047","DOIUrl":"https://doi.org/10.1142/s0129055x22300047","url":null,"abstract":"We give a pedagogical presentation of the irreducible unitary representations of C⋊Spin(4,C), that is, of the universal cover of the complexified Poincaré group C ⋊ SO(4,C). These representations were first investigated by Roffman in 1967. We provide a modern formulation of his results together with some facts from the general Wigner-Mackey theory which are relevant in this context. Moreover, we discuss different ways to realize these representations and, in the case of a non-zero “complex mass”, we give a detailed construction of a more explicit realization. This explicit realization parallels and extends the one used in the classical Wigner case of R ⋊ Spin(1, 3). Our analysis is motivated by the interest in the Euclidean formulation of Fermionic theories.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42027244","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
One-matrix differential reformulation of two-matrix models 双矩阵模型的单矩阵微分重表述
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-08-01 DOI: 10.1142/S0129055X2250026X
J. Brunekreef, L. Lionni, Johannes Thurigen
{"title":"One-matrix differential reformulation of two-matrix models","authors":"J. Brunekreef, L. Lionni, Johannes Thurigen","doi":"10.1142/S0129055X2250026X","DOIUrl":"https://doi.org/10.1142/S0129055X2250026X","url":null,"abstract":"Differential reformulations of field theories are often used for explicit computations. We derive a one-matrix differential formulation of two-matrix models, with the help of which it is possible to diagonalize the one- and two-matrix models using a formula by Itzykson and Zuber that allows diagonalizing differential operators with respect to matrix elements of Hermitian matrices. We detail the equivalence between the expressions obtained by diagonalizing the partition function in differential or integral formulation, which is not manifest at first glance. For one-matrix models, this requires transforming certain derivatives to variables. In the case of two-matrix models, the same computation leads to a new determinant formulation of the partition function, and we discuss potential applications to new orthogonal polynomials methods.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45620973","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: 1
Spectral and scattering theory for topological crystals perturbed by infinitely many new edges 被无限多新边扰动的拓扑晶体的光谱和散射理论
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-07-18 DOI: 10.1142/S0129055X22500106
S. Richard, N. Tsuzu
{"title":"Spectral and scattering theory for topological crystals perturbed by infinitely many new edges","authors":"S. Richard, N. Tsuzu","doi":"10.1142/S0129055X22500106","DOIUrl":"https://doi.org/10.1142/S0129055X22500106","url":null,"abstract":"In this paper, we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. Special attention is paid to perturbations obtained by the addition of an infinite number of edges, and/or by the removal of a finite number of them, but perturbations of the underlying measures and perturbations by the addition of a multiplication operator are also considered. The description of the nature of the spectrum of the resulting operators and the existence and completeness of the wave operators are standard outcomes for these investigations.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45362729","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
4-Manifold Topology, Donaldson–Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism 4流形拓扑、Donaldson-Witten理论、花同调和BV-BFV形式中的高规范理论方法
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-07-01 DOI: 10.1142/s0129055x22500295
Nima Moshayedi
{"title":"4-Manifold Topology, Donaldson–Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism","authors":"Nima Moshayedi","doi":"10.1142/s0129055x22500295","DOIUrl":"https://doi.org/10.1142/s0129055x22500295","url":null,"abstract":"We study the behavior of Donaldson's invariants of 4-manifolds based on the moduli space of anti self-dual connections (instantons) in the perturbative field theory setting where the underlying source manifold has boundary. It is well-known that these invariants take values in the instanton Floer homology groups of the boundary 3-manifold. Gluing formulae for these constructions lead to a functorial topological field theory description according to a system of axioms developed by Atiyah, which can be also regarded in the setting of perturbative quantum field theory, as it was shown by Witten, using a version of supersymmetric Yang-Mills theory, known today as Donaldson-Witten theory. One can actually formulate an AKSZ model which recovers this theory for a certain gauge-fixing. We consider these constructions in a perturbative quantum gauge formalism for manifolds with boundary that is compatible with cutting and gluing, called the BV-BFV formalism, which was recently developed by Cattaneo, Mnev and Reshetikhin. We prove that this theory satisfies a modified Quantum Master Equation and extend the result to a global picture when perturbing around constant background fields. Additionally, we relate these constructions to Nekrasov's partition function by treating an equivariant version of Donaldson-Witten theory in the BV formalism. Moreover, we discuss the extension, as well as the relation, to higher gauge theory and enumerative geometry methods, such as Gromov-Witten and Donaldson-Thomas theory and recall their correspondence conjecture for general Calabi-Yau 3-folds. In particular, we discuss the corresponding (relative) partition functions, defined as the generating function for the given invariants, and gluing phenomena.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46576097","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
Frobenius Objects in the Category of Spans Spans范畴中的Frobenius对象
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-06-28 DOI: 10.1142/S0129055X22500362
Iván A. Contreras, M. Keller, R. Mehta
{"title":"Frobenius Objects in the Category of Spans","authors":"Iván A. Contreras, M. Keller, R. Mehta","doi":"10.1142/S0129055X22500362","DOIUrl":"https://doi.org/10.1142/S0129055X22500362","url":null,"abstract":"We consider Frobenius objects in the category Span, where the objects are sets and the morphisms are isomorphism classes of spans of sets. We show that such structures are in correspondence with data that can be characterized in terms of simplicial sets. An interesting class of examples comes from groupoids. Our primary motivation is that Span can be viewed as a set-theoretic model for the symplectic category, and thus Frobenius objects in Span provide set-theoretic models for classical topological field theories. The paper includes an explanation of this relationship.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43786251","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: 2
Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties 特殊Scarf-I势的广义相干态:它们的时空和统计特性
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-06-26 DOI: 10.1142/S0129055X21500331
T. Shreecharan, S. Ranjani
{"title":"Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties","authors":"T. Shreecharan, S. Ranjani","doi":"10.1142/S0129055X21500331","DOIUrl":"https://doi.org/10.1142/S0129055X21500331","url":null,"abstract":"We construct generalized coherent states for the rationally extended Scarf-I potential. Statistical and geometrical properties of these states are investigated. Special emphasis is given to the study of spatio-temporal properties of the coherent states via the quantum carpet structure and the auto-correlation function. Through this study, we aim to find the signature of the “rationalization” of the conventional potentials and the classical orthogonal polynomials.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41401397","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
ACTIVIDAD FÍSICA COMO PREVENCIÓN DE SOBREPESO Y OBESIDAD EN NIÑOS DE 7-12 AÑOS. 体育活动对7-12岁儿童超重和肥胖的预防作用。
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-06-16 DOI: 10.35563/RMP.V10I1.402
Diana Mayerly Vega-Valdivieso, Karen Yulianna Amaya-Palacios, Carenth Jinneth Lineros-Florez, Graciela Olarte-Rueda
{"title":"ACTIVIDAD FÍSICA COMO PREVENCIÓN DE SOBREPESO Y OBESIDAD EN NIÑOS DE 7-12 AÑOS.","authors":"Diana Mayerly Vega-Valdivieso, Karen Yulianna Amaya-Palacios, Carenth Jinneth Lineros-Florez, Graciela Olarte-Rueda","doi":"10.35563/RMP.V10I1.402","DOIUrl":"https://doi.org/10.35563/RMP.V10I1.402","url":null,"abstract":"Introducción: La obesidad y el sobrepeso son un problema de salud que en la actualidad está afectando en gran medida a los niños y niñas a nivel mundial y nacional. Objetivo: determinar el nivel de actividad física que maneja la población escolar de 7 a 12 años en dos colegios del área rural y urbana de municipio de San Gil, para la prevención del sobrepeso y la obesidad. Materiales y métodos: Estudio cuantitativo descriptivo de corte transversal, la muestra estuvo conformada por 102 estudiantes de dos instituciones publica, pata la recolección de los datos se utilizó el instrumento para valoración del estado nutricional (sobrepeso y obesidad) por medidas antropométricas y hábitos alimentarios, tomado de una investigación de la universidad de Cartagena, se aplicó estadística descriptiva. Resultados: Se encontró que el 33,3% de los niños respondieron que hicieron actividad física 2 o 3 veces por semana, el 27,5% la realizaron 4 a 5 veces por semana, el 17,5% 6 a 7 veces por semana, 11,8% no realizaron ninguna actividad física y 9,8% 1 vez la última semana. Conclusiones: Se identificó que los escolares realizan activada física durante la semana, se encontraron casos de sobrepeso y obesidad.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"10 1","pages":"32-37"},"PeriodicalIF":1.8,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46441899","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
Reduction cohomology of Riemann surfaces Riemann曲面的归约上同调
IF 1.8 3区 物理与天体物理
Reviews in Mathematical Physics Pub Date : 2021-06-11 DOI: 10.1142/s0129055x23300054
A. Zuevsky
{"title":"Reduction cohomology of Riemann surfaces","authors":"A. Zuevsky","doi":"10.1142/s0129055x23300054","DOIUrl":"https://doi.org/10.1142/s0129055x23300054","url":null,"abstract":"We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra $n$-point functions with differential being defined through reduction formulas. The notion of the reduction cohomology of Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings of reduction formulas is clarified. A counterpart of the Bott-Segal theorem for Riemann surfaces in terms of the reductions cohomology is proven. It is shown that the reduction cohomology is given by the cohomology of $n$-point connections over the vertex operator algebra bundle defined on a genus $g$ Riemann surface $Sigma^{(g)}$. The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on $Sigma^{(g)}$ is found in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations. For the reduction cohomology, the Euler-Poincare formula is derived. Examples for various genera and vertex operator cluster algebras are provided.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47807970","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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