The wigner distribution function for systems of bosons or fermions

Abstract

An expression for the Wigner distribution function valid for systems of bosons or fermions is obtained by making use of correspondence relations between classical quantities and quantum mechanical operators first given by Groenewold. A general and straightforward derivation of the equation of motion for the Wigner distribution function is presented. The equation governing the temperature dependence of the Wigner distribution function in the case of a canonical ensemble can be derived in a completely analogous way.