Groupoids and Coherent States Articles uri icon

publication date

  • February 2020

issue

  • 4(1950017)

volume

  • 26

International Standard Serial Number (ISSN)

  • 1230-1612

abstract

  • 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.

keywords

  • coherent states; groupoids; schwinger algebra