Calculation of the single-particle Green's function of interacting fermions in arbitrary dimension via functional bosonization
Abstract
Description
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 $ϕ^α$. 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 $ϕ^α$-field and then averaging the resulting expression with respect to the probability distribution ${\cal{P}} \{ ϕ^α \} \propto \exp [ - S_{eff} \{ ϕ^α \} ]$, where $S_{eff} \{ ϕ^α \}$ is the effective action of the $ϕ^α$-field. We emphasize the approximations inherent in the higher-dimensional bosonization approach and clarify its relation with diagrammatic perturbation theory.
compressed postscript file, 4 figures included. This is a written version of a talk I gave at the Raymond L. Orbach Symposium, Riverside, Ca, March 18, 1995. To be published in the Proceedings of the Orbach Symposium, World Scientific. Editor: D. Hone
compressed postscript file, 4 figures included. This is a written version of a talk I gave at the Raymond L. Orbach Symposium, Riverside, Ca, March 18, 1995. To be published in the Proceedings of the Orbach Symposium, World Scientific. Editor: D. Hone