# Groupoids and Coherent states

## TL;DR

This paper demonstrates that the theory of coherent states can be naturally formulated within the framework of groupoids, linking Schwinger's measurement algebra to quantum state representations.

## Contribution

It introduces a groupoid-based framework for coherent states, generalizing their construction beyond traditional settings and including examples like harmonic oscillators and f-oscillators.

## Key findings

- Standard harmonic oscillator coherent states are recovered
- Generalized coherent states for f-oscillators are constructed
- Invariant subsets of the groupoid algebra determine coherent states

## 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.