Algebraic formulation of local temperature states

为了阐明布赫霍尔茨和我在[2]中发现的自发对称性坍缩的物理和数学意义，我在1997年详细阐述了热力学相之间的关系、区分不同相的序参量、表示代数的中心和系统的对称性等基本问题。我发现的是有用的结果涉及频谱的中心，中央遍历性和近似序列的本地运营商倾向于中心的元素，这表现出有趣的角色的基本概念在量子概率论中的大偏差时，适用于讨论与低能量定理。1998年上半年，我受哥廷根科学院的邀请，在哥廷根大学担任高斯教授，与布赫霍尔茨和鲁什教授合作研究了量子力学中的量子力学问题。 关于我们 我还详细阐述了对称性破缺模式的分类[5]，它通过将[2]的结果放在更广泛的角度来回答上述问题，其中所有可能的对称性破缺模式都被排除和分类。关于前者，其大纲已在RIMS-“量子信息和量子混沌数学”会议上报告，并正在编写一份联合文件。其思想是通过在每个时空点的小邻域中的适当的局部可观测量族将给定的状态映射到所有KMS状态的集合，以将其表示为各种KMS状态的混合物，通过这种混合物，以一种新的方式获得热平衡的局部版本。在无质量标量场模型中有一个这样的局部温度态的非平凡例子，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前途的方向。在1998年秋天，我曾与教授讨论。S.Maumary在Univ.de洛桑的一个同源代数重新制定的BRS上同调，我们一直在继续一个联合项目，以完成这项工作。少

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