Bosonization of Fermi liquids

TL;DR

This paper develops a bosonization approach for Fermi liquids across any dimensions, providing a new framework to analyze their excitations, thermodynamics, and collective behaviors.

Contribution

It introduces a bosonization method for Fermi liquids in arbitrary dimensions and constructs a path integral formalism that captures their thermodynamic and dynamical properties.

Findings

Quadratic bosonic Hamiltonian for interacting fermions

Path integral reproduces Landau's sound wave equation

Correct specific heat form for Fermi liquids

Abstract

We bosonize a Fermi liquid in any number of dimensions in the limit of long wavelengths. From the bosons we construct a set of coherent states which are related with the displacement of the Fermi surface due to particle-hole excitations. We show that an interacting hamiltonian in terms of the original fermions is quadratic in the bosons. We obtain a path integral representation for the generating functional which in real time, in the semiclassical limit, gives the Landau equation for sound waves and in the imaginary time gives us the correct form of the specific heat for a Fermi liquid even with the corrections due to the interactions between the fermions. We also discuss the similarities between our results and the physics of quantum crystals.