Functional Bosonization of Interacting Fermions in Arbitrary Dimensions

TL;DR

This paper presents a novel bosonization method for interacting fermions in any dimension, providing a simple expression for the Green's function that captures both Fermi and Luttinger liquids, and offers insights into screening and RPA relations.

Contribution

It introduces a direct Hubbard-Stratonovich bosonization technique applicable in arbitrary dimensions, unifying descriptions of Fermi and Luttinger liquids.

Findings

Derived a simple Green's function expression valid for all interaction strengths.

Unified description of Fermi and Luttinger liquids in arbitrary dimensions.

Provided a non-perturbative approach to screening phenomena.

Abstract

We bosonize the long-wavelength excitations of interacting fermions in arbitrary dimension by directly applying a suitable Hubbard-Stratonowich transformation to the Grassmannian generating functional of the fermionic correlation functions. With this technique we derive a surprisingly simple expression for the single-particle Greens-function, which is valid for arbitrary interaction strength and can describe Fermi- as well as Luttinger liquids. Our approach sheds further light on the relation between bosonization and the random-phase approximation, and enables us to study screening in a non-perturbative way.