Decoupling Transformations in Path Integral Bosonization

TL;DR

This paper introduces a method to decouple fermionic fields from gauge interactions in path integrals, enabling explicit bosonization of fermionic models in various dimensions, including a novel 3D approach.

Contribution

It presents a general decoupling transformation applicable in any dimension and extends bosonization techniques to three-dimensional models with explicit fermion-boson relations.

Findings

Decoupling transformations expressed as non-local functionals of gauge fields.

Explicit bosonization of the 3D Thirring model with fermion fields in terms of bosonic variables.

Connection established between the new technique and traditional 2D decoupling methods.

Abstract

We construct transformations that decouple fermionic fields in interaction with a gauge field, in the path integral representation of the generating functional. Those transformations express the original fermionic fields in terms of non-interacting ones, through non-local functionals depending on the gauge field. This procedure, holding true in any number of spacetime dimensions both in the Abelian and non-Abelian cases, is then applied to the path integral bosonization of the Thirring model in 3 dimensions. Knowledge of the decoupling transformations allows us, contrarily to previous bosonizations, to obtain the bosonization with an explicit expression of the fermion fields in terms of bosonic ones and free fermionic fields. We also explain the relation between our technique, in the two dimensional case, and the usual decoupling in 2 dimensions.