Smooth Bosonization II: The Massive Case

TL;DR

This paper extends bosonization techniques to include massive fermions in (1+1) dimensions, deriving exact relations by gauge fixing and solving a strongly coupled Schwinger model.

Contribution

It introduces a method to derive bosonization relations for massive fermions using gauge fixing, providing exact solutions for the bosonic counterparts of fermionic mass terms.

Findings

Derived bosonization relations for massive fermions.

Solved the strongly coupled Schwinger model exactly.

Established bosonic counterparts of fermionic mass densities.

Abstract

The (1+1)-dimensional bosonization relations for fermionic mass terms are derived by choosing a specific gauge in an enlarged gauge-invariant theory containing both fermionic and bosonic fields. The fermionic part of the generating functional subject to the gauge constraint can be cast into the form of a strongly coupled Schwinger model, which can be solved exactly. The resulting bosonic theory coupled to the scalar sources then exhibits directly the bosonic counterparts of the fermionic scalar and pseudoscalar mass densities.