Collective Variables of Fermions and Bosonization

TL;DR

This paper introduces a universal method for deriving collective variables in fermionic systems, leading to a bosonized description that is independent of specific potential details, applicable in large particle number limits.

Contribution

It extends gauge theory of collective coordinates to fermions and derives a universal bosonization Lagrangian for non-interacting flavored fermions in one dimension.

Findings

Derives a collective variable extraction method for fermions.

Obtains a Wess-Zumino-Witten type Lagrangian in the large particle limit.

Shows universality of the bosonization result regardless of potential details.

Abstract

We first present a general method for extracting collective variables out of non-relativistic fermions by extending the gauge theory of collective coordinates to fermionic systems. We then apply the method to a system of non-interacting flavored fermions confined in a one-dimensional flavor-independent potential. In the limit of a large number of particles we obtain a Lagrangian with the Wess-Zumino-Witten term, which is the well-known Lagrangian describing the non-Abelian bosonization of chiral fermions on a circle. The result is universal and does not depend on the details of the confining potential.