WIGNER FUNCTIONS IN COVARIANT AND SINGLE-TIME FORMULATIONS

We will establish the connection between the Lorentz covariant and so- called single-time formulation for the quark Wigner operator. To, this end we will discuss the initial value problem for the Wigner operator of a field theory and give a discussion of the gauge-covariant formul ation for the Wigner operator including some new results concerning th e chiral limit. We discuss the gradient or semi-classical expansion an d the color and spinor decomposition of the equations of motion for th e Wigner operator. The single-time formulation will be derived from th e covariant formulation by taking energy moments oi the equations for the Wigner operator. For external fields we prove that only the lowest energy moments of the quark Wigner operator contain dynamical informa tion. (C) 1998 Academic Press.