Bosonization of Fermi Systems in Arbitrary Dimension in Terms of Gauge Forms

TL;DR

This paper introduces a universal bosonization method for Fermi systems in any dimension using gauge theory concepts, enabling new analytical tools for condensed matter physics.

Contribution

It develops a general bosonization framework for fermions in arbitrary dimensions using gauge fields, connecting condensed matter systems with gauge theory techniques.

Findings

Exact formula for the plasmon gap in metals

Derivation of the Anderson-Higgs mechanism in superconductors

Analysis of the orthogonality catastrophe for static sources

Abstract

We present a general method to bosonize systems of Fermions with infinitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, by expressing the quantized conserved electric charge- and current density in terms of a bosonic antisymmetric tensorfield of a rank d--1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analyzing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such as Wegner -'t Hooft duality, to a variety of systems of condensed matter physics: Landau-Fermi liquids, Hall fluids, London superconductors, etc.. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.