Reviews in Mathematical Physics最新文献_第9页

Hopf Algebroids from Noncommutative Bundles 非交换束中的Hopf代数群

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2022-01-05 DOI: 10.1142/s0129055x23500277

Xiao-Wei Han, Giovanni Landi, Yang Liu

引用次数: 1

Symmetric states for C*-fermi systems C*-费米系统的对称态

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2022-01-02 DOI: 10.1142/S0129055X22500301

F. Fidaleo

{"title":"Symmetric states for C*-fermi systems","authors":"F. Fidaleo","doi":"10.1142/S0129055X22500301","DOIUrl":"https://doi.org/10.1142/S0129055X22500301","url":null,"abstract":"In the present note, which is the second part of a work concerning the study of the set of the symmetric states, we introduce the extension of the Klein transformation for general Fermi tensor product of two Z graded C-algebras, under the condition that the grading of one of the involved algebras is inner. After extending the construction to C-inductive limits, such a Klein transformation realises a canonical ∗-isomorphism between two Z-graded C-algebras made of the infinite Fermi C-tensor product AF := ( F N B, F N α ) , and the infinite C-tensor product AX := ( X N B, X N α ) of a single Z-graded C-algebra (B, α), both built with respect to the corresponding minimal C-cross norms. It preserves the grading, and its transpose sends even product states of AX in (necessarily even) product states on AF, and therefore induces an isomorphism of simplexes SP(AF) = SP×Z2(AF) ∼ SP×Z2(AX) , which allows to reduce the study of the structure of the symmetric states for C-Fermi systems to the corresponding even symmetric states on the usual infinite C-tensor product. Other relevant properties of symmetric states on the Fermi algebra will be proved without the use of the Klein transformation. We end with an example for which such a Klein transformation is not implementable, simply because the Fermi tensor product does not generate a usual tensor product. Therefore, in general, the study of the symmetric states on the Fermi algebra cannot be reduced to that of the corresponding symmetric states on the usual infinite tensor product, even if both share many common properties. Mathematics Subject Classification: 46L53, 46L05, 60G09, 46L30, 46N50.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48039045","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

Correlation Inequalities for the Uniform 8-Vertex Model and the Toric Code Model 一致8顶点模型与环面码模型的相关不等式

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2022-01-01 DOI: 10.1142/s0129055x23500290

J. Bjornberg, Benjamin Lees

引用次数: 0

Continuous Dependence on the Initial Data in the Kadison Transitivity Theorem and GNS Construction Kadison传递定理中初始数据的连续依赖性及GNS的构造

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-12-26 DOI: 10.1142/S0129055X22500313

D. Spiegel, J. Moreno, Marvin Qi, M. Hermele, A. Beaudry, M. Pflaum

{"title":"Continuous Dependence on the Initial Data in the Kadison Transitivity Theorem and GNS Construction","authors":"D. Spiegel, J. Moreno, Marvin Qi, M. Hermele, A. Beaudry, M. Pflaum","doi":"10.1142/S0129055X22500313","DOIUrl":"https://doi.org/10.1142/S0129055X22500313","url":null,"abstract":"We consider how the outputs of the Kadison transitivity theorem and Gelfand-Naimark-Segal construction may be obtained in families when the initial data are varied. More precisely, for the Kadison transitivity theorem, we prove that for any nonzero irreducible representation $(mathcal{H}, pi)$ of a $C^*$-algebra $mathfrak{A}$ and $n in mathbb{N}$, there exists a continuous function $A:X rightarrow mathfrak{A}$ such that $pi(A(mathbf{x}, mathbf{y}))x_i = y_i$ for all $i in {1, ldots, n}$, where $X$ is the set of pairs of $n$-tuples $(mathbf{x}, mathbf{y}) in mathcal{H}^n times mathcal{H}^n$ such that the components of $mathbf{x}$ are linearly independent. Versions of this result where $A$ maps into the self-adjoint or unitary elements of $mathfrak{A}$ are also presented. Regarding the Gelfand-Naimark-Segal construction, we prove that given a topological $C^*$-algebra fiber bundle $p:mathfrak{A} rightarrow Y$, one may construct a topological fiber bundle $mathscr{P}(mathfrak{A}) rightarrow Y$ whose fiber over $y in Y$ is the space of pure states of $mathfrak{A}_y$ (with the norm topology), as well as bundles $mathscr{H} rightarrow mathscr{P}(mathfrak{A})$ and $mathscr{N} rightarrow mathscr{P}(mathfrak{A})$ whose fibers $mathscr{H}_omega$ and $mathscr{N}_omega$ over $omega in mathscr{P}(mathfrak{A})$ are the GNS Hilbert space and closed left ideal, respectively, corresponding to $omega$. When $p:mathfrak{A} rightarrow Y$ is a smooth fiber bundle, we show that $mathscr{P}(mathfrak{A}) rightarrow Y$ and $mathscr{H}rightarrow mathscr{P}(mathfrak{A})$ are also smooth fiber bundles; this involves proving that the group of $*$-automorphisms of a $C^*$-algebra is a Banach-Lie group. In service of these results, we review the geometry of the topology and pure state space. A simple non-interacting quantum spin system is provided as an example.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47428212","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

The second law of thermodynamics as a deterministic theorem for quantum spin systems 热力学第二定律作为量子自旋系统的确定性定理

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-12-02 DOI: 10.1142/s0129055x22300059

W. Wreszinski

引用次数: 1

The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition 非Fredholm条件下一维分步量子行走的Witten指数

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-11-07 DOI: 10.1142/S0129055X23500101

Yasumichi Matsuzawa, A. Suzuki, Yohei Tanaka, Noriaki Teranishi, K. Wada

引用次数: 1

Yang–Mills theories on geometric spaces 几何空间的杨-米尔斯理论

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-10-25 DOI: 10.1142/s0129055x22300011

Yalong Cao

引用次数: 0

Rigid Body with Rotors and Reduction by Stages 带转子和分级减速的刚体

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-10-21 DOI: 10.1142/s0129055x22300060

Miguel Angel Berbel, M. L'opez

引用次数: 0

Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model 正则化Nelson模型的Bogoliubov动力学和高阶修正

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-10-01 DOI: 10.1142/s0129055x2350006x

M. Falconi, Nikolai Leopold, D. Mitrouskas, S. Petrat

引用次数: 5

Spectral enclosures for Dirac operators perturbed by rigid potentials 刚性势扰动Dirac算子的谱包络

IF 1.8 3区物理与天体物理

Reviews in Mathematical Physics Pub Date : 2021-08-29 DOI: 10.1142/S0129055X22500234

H. Mizutani, N. Schiavone

引用次数: 2