Wigner function for the coherent states of a particle on a circle

Abstract

This paper aims to dicuss on the construction of Wigner function for coherent states of a particle on a circle. These coherent states are computed using unitary irreducible representation Û(σ, ℓ) taking the role of Weyl operators as discussed by Perelomov. From the constructed coherent states a Wigner function will then be computed.