Wigner functions on Euclidean motion group of rank three

Abstract

In this paper, we compute the Wigner operator and Wigner function on the Euclidean motion group of rank three. The Wigner quasiprobability distribution is one of the main ingredients in phase space quantum mechanics and has found numerous applications. Generalizations of it in the Lie group setting remains an important problem in physics and mathematics, to which this work makes a contribution.