基于选择准则的广义扇形统一格式--对称性和热性的序参量及双折射的物理意义
A Unified Scheme for Generalized Sectors based on Selection Criteria --Order parameters of symmetries and of thermality and physical meanings of adjunctions--
摘要：
基于选择准则的概念，本文提出了一个统一的处理广义超选择扇区的方案，用以描述量子物理中各个特定领域的相关态，从内部对称性未破缺和自发破缺的真空情形下的相对论量子场，到平衡态和非平衡态，再到测量过程中的一些基本方面。这是通过c-q和q-c通道的帮助来实现的：前者确定要选择的状态和要由序参量参数化的状态，后者根据序参量提供所选状态的物理解释。这个公式扩展了传统的多普利歇-罗伯茨构造方法恢复场代数和规范群的适用范围（第一类）从群不变观测量的数据到自发对称性破缺的情况：在所提出的机制的使用中，与自发破缺对称性相关联的基本结构成分的物理和数学意义被重新检验，如由属于相应齐次空间的变量参数化的退化真空、Goldstone模和凝聚等。序参量空间的几何意义与作为扇形结构的分类空间的附连关系自然地理解。作为应用的进一步例子，在量子理论的数学框架中出现的一些基本概念被重新表述，并与控制理论相结合进行了研究。
英文摘要：
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic quantum fields in the vacuum situations with unbroken and spontaneously broken internal symmetries, through equilibrium and non-equilibrium states to some basic aspects in measurement processes. This is achieved by the help of c-q and q-c channels: the former determines the states to be selected and to be parametrized by the order parameters, and the latter provides the physical interpretations of selected states in terms of order parameters. This formulation extends the traditional range of applicability of the Doplicher-Roberts construction method for recovering the field algebra and the gauge group (of the first kind) from the data of group invariant observables to the situations with spontaneous symmetry breakdown: in use of the machinery proposed, the physical and mathematical meaning of basic structural ingredients associated with the spontaneously broken symmetry are re-examined, such as the degenerate vacua parametrized by the variable belonging to the relevant homogeneous space, the Goldstone modes and condensates, etc. The geometrical meaning of the space of order parameters is naturally understood in relation with the adjunction as the classifying space of a sector structure. As further examples of applications, some basic notions arising in the mathematical framework of quantum theory are reformulated and examined in connection with control theory.
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