群胚与相干态
Groupoids and Coherent states
摘要：
施温格的选择性测量代数在群胚方面有一个自然的解释。本文提出的这种方法表明相干态理论在群胚的框架下有一个自然的背景。因此，给定一个量子力学系统与相关的希尔伯特空间所确定的表示的广群，它表明，任何不变的子集群的可逆元素在广群代数确定一个家庭的广义相干态提供了一个完整性条件得到满足。谐振子的标准相干态以及f-振子的广义相干态都在这幅图中举例说明。
英文摘要：
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.
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