No-ghost theorem for the fourth-order derivative pais-uhlenbeck oscillator model
No-ghost theorem for the fourth-order derivative pais-uhlenbeck oscillator model
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DOI：
10.1103/physrevlett.100.110402
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发表时间：
2008-03-21
影响因子：
8.6
通讯作者：
Mannheim, Philip D.
中科院分区：
文献类型：
--
作者：
Bender, Carl M.;Mannheim, Philip D.
构造了四阶导数Pais-Uhlenbeck振子的一种新实现。这种实现不具有负范数的状态，并且具有下有界的真实的能谱。这种构造的关键是认识到在这种实现中，哈密尔顿算子不是狄拉克厄米算子。然而，在空间反射P和时间反演T的组合下，哈密顿量是对称的。希尔伯特空间，这是适当的PT-对称的哈密顿量被确定，它被发现有一个正定的内积。此外，时间演化算子是酉的。
A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed. This realization possesses no states of negative norm and has a real energy spectrum that is bounded below. The key to this construction is the recognition that in this realization the Hamiltonian is not Dirac Hermitian. However, the Hamiltonian is symmetric under combined space reflection P and time reversal T. The Hilbert space that is appropriate for this PT-symmetric Hamiltonian is identified and it is found to have a positive-definite inner product. Furthermore, the time-evolution operator is unitary.