代数量子理论中的经典极限与自发对称性破缺
The classical limit and spontaneous symmetry breaking in algebraic quantum theory
摘要：
本文综述了代数量子理论中经典极限和自发对称性破缺（SSB）的一些最新进展。在这些工作中，基于$C^*$ -代数的理论，经典极限的概念已被形式化在一个完整的代数方式。此外，由于这种设置允许交换以及非交换的$C^*$ -代数，因此对于经典和量子理论，它提供了一个很好的框架来研究SBB作为一个新兴的现象时，从量子过渡到经典世界关闭半经典参数。我们总结的主要结果，并表明，这种代数方法揭示了新的光之间的连接的经典和量子领域，特别强调的是放在SSB的作用理论与自然。为此，进行了详细的分析，并说明了三种不同的物理模型：薛定谔运营商，平均场量子自旋系统和玻色-哈伯德模型。
英文摘要：
In this paper an overview of some recent developments on the classical limit and spontaneous symmetry breaking (SSB) in algebraic quantum theory is given. In such works, based on the theory of $C^*$-algebras, the concept of the classical limit has been formalized in a complete algebraic manner. Additionally, since this setting allows for commutative as well as non-commutative $C^*$-algebras, and hence for classical and quantum theories, it provides an excellent framework to study SBB as an emergent phenomenon when transitioning from the quantum to the classical world by turning off a semi-classical parameter. We summarize the main results and show that this algebraic approach sheds new light on the connection between the classical and the quantum realm, where particular emphasis is placed on the role of SSB in Theory versus Nature. To this end a detailed analysis is carried out and illustrated with three different physical models: Schrödinger operators, mean-field quantum spin systems and the Bose-Hubbard model.
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