On the operator bases underlying Wigner's, Kirkwood's and Glauber's phase space functions

Abstract

The Hermitian operators behind Wigner's phase space function (1932) are recognised to be simple ordered exponentials of the dynamical variables. This operator basis is highly symmetric; it supplies a perfectly unbiased formulation of operator equations in terms of phase space functions, which is as close to classical physics as it possibly can be. The author demonstrates how the symmetry properties of the basis can be exploited to simplify the computation of Wigner functions enormously. The ordered-operator methods are also applicable to the phase space functions of Kirkwood (1933) and Glauber (1963) type. Both kinds are briefly discussed with emphasis on how they differ from Wigner's description.