  The closed time-path (CTP) formalism is a powerful Green's function
formulation to describe nonequilibrium phenomena in field theory and it leads
to a complete nonequilibrium quantum kinetic theory. In this paper we make use
of the CTP formalism to write down a set of quantum Boltzmann equations
describing the local number density asymmetries of the particles involved in
supersymmetric electroweak baryogenesis. These diffusion equations
automatically and self-consistently incorporate the CP-violating sources which
fuel baryogenesis when transport properties allow the CP-violating charges to
diffuse in front of the bubble wall separating the broken from the unbroken
phase at the electroweak phase transition. This is a significant improvement
with respect to recent approaches where the CP-violating sources are inserted
by hand into the diffusion equations. Furthermore, the CP-violating sources and
the particle number changing interactions manifest ``memory'' effects which are
typical of the quantum transp ort theory and are not present in the classical
approach. The slowdown of the relaxation processes may keep the system out of
equilibrium for longer times and therefore enhance the final baryon asymmetry.
We also stress that the classical approximation is not adequate to describe the
quantum interference nature of CP-violation and that a quantum approach should
be adopted to compute the sources since they are most easily built up by the
transmission of low momentum particles.
