Bosonization of the Low Energy Excitations of Fermi Liquids

TL;DR

This paper develops a bosonization approach for low energy excitations in Fermi liquids across dimensions, representing Fermi surface deformations with coherent bosonic states and deriving an exact semiclassical Landau equation.

Contribution

It introduces a general bosonization method for Fermi liquids in any dimension, linking bosonic excitations to Fermi surface displacements and deriving a path integral formulation.

Findings

Bosons are coherent superpositions of electron-hole pairs.

The path integral describes Fermi surface shape histories.

The Landau sound wave equation is exact semiclassically.

Abstract

We bosonize the low energy excitations of Fermi Liquids in any number of dimensions in the limit of long wavelengths. The bosons are coherent superposition of electron-hole pairs and are related with the displacement of the Fermi Surface in some arbitrary direction. A coherent-state path integral for the bosonized theory is derived and it is shown to represent histories of the shape of the Fermi Surface. The Landau equation for the sound waves is shown to be exact in the semiclassical approximation for the bosons.