PT-对称性、CPT-内积和赝厄米性的Krein空间表示
Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
摘要：
强调的物理约束制定的量子理论的基础上的标准测量公理和薛定谔方程，我们评论的PT对称量子力学制定中出现的一些概念问题。特别是，我们详细说明了度量算子的有界性和哈密顿量的对角化的要求。我们还提供了一个可访问的帐户的克莱因空间推导的CPT-内积，这是众所周知的数学家自20世纪50年代。我们展示了这个推导是如何与PT对称量子力学的伪厄米公式联系在一起的。
英文摘要：
Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.
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