  The single-particle Green's function of an interacting Fermi system with
dominant forward scattering is calculated by decoupling the interaction by
means of a Hubbard-Stratonowich transformation involving a bosonic auxiliary
field $\phi^{\alpha}$. We obtain a higher dimensional generalization of the
well-known one-dimensional bosonization result for the Green's function by
first calculating the Green's function for a fixed configuration of the
$\phi^{\alpha}$-field and then averaging the resulting expression with respect
to the probability distribution ${\cal{P}} \{ \phi^{\alpha} \} \propto \exp [ -
S_{eff} \{ \phi^{\alpha} \} ]$, where $S_{eff} \{ \phi^{\alpha} \}$ is the
effective action of the $\phi^{\alpha}$-field. We emphasize the approximations
inherent in the higher-dimensional bosonization approach and clarify its
relation with diagrammatic perturbation theory.
