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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Groupoids 和相干状态

施温格的选择性测量代数在群方面有一个自然的解释。本文提出了这种方法，以表明相干态理论在群形框架中具有自然背景。因此，给定一个具有由群样表示确定的关联希尔伯特空间的量子力学系统，表明如果满足完备性条件，群样代数中可逆元素群的任何不变子集都确定了广义相干态族。这张图片举例说明了谐振子的标准相干状态以及 f 振荡器的广义相干状态。