It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a 𝒫𝒯-symmetric Hamiltonian can also define a physically acceptable quantum-mechanical system even if the Hamiltonian is not Hermitian. The study of 𝒫𝒯-symmetric quantum systems is a young and extremely active research area in both theoretical and experimental physics. The purpose of this review is to provide established scientists as well as graduate students with a compact, easy-to-read introduction to this field that will enable them to understand more advanced publications and to begin their own theoretical or experimental research activity. The ideas and techniques of 𝒫𝒯 symmetry have been applied in the context of many different branches of physics. This review introduces the concepts of 𝒫𝒯 symmetry by focusing on elementary one-dimensional 𝒫𝒯-symmetric quantum and classical mechanics and relies, in particular, on oscillator models to illustrate and explain the basic properties of 𝒫𝒯-symmetric quantum theory.

中文翻译：

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PT - 对称量子力学


通常假设物理上可接受的量子系统（具有正定频谱并遵循幺正性要求的量子系统）的哈密顿量必须是 Hermitian。但是，PT 对称哈密顿量也可以定义物理上可接受的量子力学系统，即使哈密顿量不是厄米特量。PT 对称量子系统的研究在理论和实验物理学中都是一个年轻且极其活跃的研究领域。本综述的目的是为知名科学家和研究生提供该领域的紧凑、易于阅读的介绍，使他们能够理解更高级的出版物并开始自己的理论或实验研究活动。PT 对称性的思想和技术已应用于物理学的许多不同分支。本文通过重点介绍基本的一维 PT 对称量子和经典力学来介绍 PT 对称性的概念，特别是依靠振荡器模型来说明和解释 PT 对称量子理论的基本性质。