Calculation of the average Green's function of electrons in a stochastic medium via higher-dimensional bosonization

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 to 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.