带加速度的Action II：欧几里德哈密顿量和若当块
Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks
摘要：
文[1]中分析了加速度作用量的哈密顿量和路径积分，以下引作参考文献I。在本文中，状态空间的哈密尔顿分析的情况下，它是伪厄米（等价于厄米哈密尔顿），以及当它是不等价的。传播子是使用创建/销毁操作符以及路径积分计算的。传播子的状态空间计算显示了对偶状态向量所起的关键作用，该对偶状态向量产生的结果不可能从作用于希尔伯特空间的埃尔米特哈密顿量获得。当它不是伪厄米时，哈密顿量是Jordan块的直和。
英文摘要：
The Euclidean action with acceleration has been analyzed in [1], hereafter cited as reference I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation/destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian acting on a Hilbert space. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.
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