Algebraic formulation of local temperature states

局部温度状态的代数表述

• 批准号: 09640262
• 负责人: OJIMA Izumi
• 金额: $ 1.02万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640262/
• 关键词: Classification of symmetry breaking patterns; Spontaneous symmetry collapse; Algebraic quantum field theory; Quantum statistical mechanics; Local temperatrue states; Relativistic thermodynamics; 対称性の破れ; Algebraic QFT; Local Quantum Physics; Therm

To clarify the physical and mathematical meanings of spontaneous symmetry collapse discovered by D.Buchholz and myself in [2], I elaborated in 1997 on fundamental issues concerning relations among thermodynamic phases, order parameters to distinguish different phases, center of represented algebras and symmetry of systems. What I found is useful results involving the spectrum of centre, central ergodicity and approximate sequences of local operators tendeing to central elements, which exhibit interesting roles of the basic notions in quantum probability theory in connection with large deviations when applied to the discussions with low energy theorems. While some of these were reported in [3], I have been elaboraing on basic points in quantum-theoretical extensions of large deviation principle.In the former half of 1998, 1 was invited by Academy of Sciences in Gottingen as Gauss Professor at Gottingen University where I collaborated with Profs.D.Buchholz and H.Roos on the mathematical … More formulation of local temperature states in algebraic QFT.I also elaborated upon the classification of symmetry breaking patterns [5], which answers the above-mentioned question by placing the result of [2] in a wider perspective with all possible patterns of symmetry breaking exhausted and classified. Concerning the former, its outline was reported at RIMS-meeting of "Mathematics of Quantum Information and Quantum Chaos" and a joint paper is in preparation. The idea is to map a given state to the set of all KMS states via suitable family of local observables in small neighbourhoods of each spacetime point to represent it as a mixture of various KMS states, through which a localized version of thermal equilibrium is attained in a novel way. There is a nontrivial example of such a local temperature state in the massless scalar field model which shows interesting aspects of nonequilibrium suggesting some promising direction of general-relativistic extension of thermodynamics and quantum statistical mechanicss. In the autumn of 1998, I had discussions with Prof.S.Maumary at Univ.de Lausanne on a homological-algebraic reformulation of BRS cohomology and we have been continuing a joint project to complete this work. Less

为了阐明D.Buchholz和我在[2]中发现的对称性自发崩塌的物理和数学意义，我在1997年阐述了热力学相之间的关系、区分不同相的序参数、表示代数的中心和系统的对称性等基本问题。我发现了一些有用的结果，包括中心的谱、中心遍历和趋向中心元素的局部算子的近似序列，这些结果展示了量子概率论中与大偏差有关的基本概念在应用于低能定理的讨论中所起的有趣作用。虽然其中一些在[3]中有报道，但我一直在阐述大偏差原理的量子理论扩展的基本点。1998年上半年，1应哥廷根科学院的邀请担任哥廷根大学的高斯教授，在那里我与D.Buchholz教授和H.Roos教授在数学…方面进行了合作在代数QFT中对局域温度态的更多表述。我还阐述了对称破缺模式的分类[5]，它通过将[2]的结果放在更广泛的角度来回答上述问题，并对所有可能的对称破缺模式进行了穷尽和分类。关于前者，在RIMS“量子信息的数学和量子混沌”会议上报告了它的概要，并正在准备一篇联合论文。其思想是通过在每个时空点的小邻域中通过适当的局域可观测族将给定态映射到所有KMS态的集合，以将其表示为各种KMS态的混合物，从而以一种新颖的方式获得局域化版本的热平衡。在无质量标量场模型中，有一个这样的局域温度状态的例子，它显示了非平衡的有趣方面，表明了热力学和量子统计力学的广义相对论扩展的一些有希望的方向。1998年秋天，我与洛桑大学的莫马里教授讨论了BRS上同调的同调-代数重新表述，我们一直在继续一个联合项目来完成这项工作。较少

项目成果

Izumi Ojima: "Order parameters and large deviation in QFT" RIMS Kokyuroku No.1066 "Quantum Probability & Entropic Analysis". 121-132 (1998)

小岛泉：《QFT 中的有序参数和大偏差》RIMS Kokyuroku No.1066《量子概率》

Izumi Ojima: "Symmetry Breaking Patterns-Spontaneous Collapse of SUSY and Othersーー" in “Classical and Quantum White Noise"(eds.L.Accardi, H.-H.Kuo, L.Streit, Si Si and K. Saito) (Kluwer Publishing Company). (刊行予定).

Izumi Ojima：“经典和量子白噪声”中的“对称破缺模式 - SUSY 等的自发崩溃”（eds.L.Accardi、H.-H.Kuo、L.Streit、Si Si 和 K. Saito）（Kluwer）出版公司）（待出版）。

D.Buchholz and I.Ojima: "Spontaneous Collapse of Supersymmetry" Nuclear Physics. B498. 228-242 (1997)

D.Buchholz 和 I.Ojima：“超对称性的自发塌缩”核物理。

Izumi Ojima: "Spontaneous Collapse of Supersymmetry" in Proc.of 2nd Jagna Intern. Workshop on “Mathematical Methods of Quantum Physics" (edited by C.C.Bernido, et al.)(Gordon & Breach). (刊行予定).

Izumi Ojima：“超对称的自发崩溃”，第二届 Jagna 实习生研讨会“量子物理的数学方法”（由 C.C.Bernido 等人编辑）（Gordon & Breach）。

Izumi Ojima: "Spontaneous Collapse of Supersymmetry" Proc.2nd Jagna Intern. Workshop on "Mathematical Methods of Quantum Physics" (edited by C.C.Bernido, et al.). (to be published by Gordon & Breach).

小岛泉：“超对称性的自发崩溃”Proc.2nd Jagna Intern。