A generalized Wigner function on the space of irreducible representations of the Weyl–Heisenberg group and its transformation properties

Abstract

A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl–Heisenberg group is discussed. The action of the automorphisms group of the Weyl–Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations.