Physics – Condensed Matter
Scientific paper
1995-06-28
Proceedings of the Raymond L. Orbach Symposium, p. 101-119, edited by D. Hone (World Scientific, Singapore, 1996)
Physics
Condensed Matter
compressed postscript file, 4 figures included. This is a written version of a talk I gave at the Raymond L. Orbach Symposium,
Scientific paper
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.
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