Complex extension of quantum mechanics
Complex extension of quantum mechanics
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DOI：
10.1103/physrevlett.89.270401
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发表时间：
2002-12-30
影响因子：
8.6
通讯作者：
Jones, HF
中科院分区：
文献类型：
--
作者：
Bender, CM;Brody, DC;Jones, HF
要求一个哈密尔顿算子是厄米算子是过于严格的。一个相容的量子力学物理理论可以建立在一个复杂的哈密顿量上，这个哈密顿量不是厄米的，但满足时空反射对称性（PT对称性）的限制较少和更多的物理条件。人们可能会期望非厄米哈密顿量导致对么正性的破坏。然而，如果PT对称性不是自发破缺的，那么就有可能构造出一个以前未被注意到的哈密顿量的对称性C。使用C，可以构造一个其相关范数为正定的内积。该过程是通用的，适用于任何PT对称哈密顿。观测量表现出CPT对称性，动力学是由酉时间演化。这项工作与传统的量子力学并不冲突，而是对它的一种复杂的推广。
Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.