  The disorder averaged single-particle Green's function of electrons subject
to a time-dependent random potential with long-range spatial correlations is
calculated by means of bosonization in arbitrary dimensions. For static
disorder our method is equivalent with conventional perturbation theory based
on the lowest order Born approximation. For dynamic disorder, however, we
obtain a new non-perturbative expression for the average Green's function.
Bosonization also provides a solid microscopic basis for the description of the
quantum dynamics of an interacting many-body system via an effective stochastic
model with Gaussian probability distribution.
