  We report on a work in progress, whose goal is a systematic field theoretical
derivation of the quantum transport equations for baryon production in the
electroweak plasma at a first order phase transition in the limit of slowly
varying background fields (thick wall limit). We start with the Schwinger-Dyson
equations for the two point Green function written in the closed time contour
(CTC) formalism. The quantum Boltzmann equations for the density matrix arise
when the SD-equations are expanded to the first order in the gradients in the
on-shell limit. In this paper we consider only scalar fields, but the formalism
can easily be extended to fermions.
