Explicit Bosonization of the Massive Thirring Model in 3+1 Dimensions

TL;DR

This paper develops an explicit bosonization method for the Massive Thirring Model in 3+1 dimensions, providing exact formulas and analyzing different mass regimes, thus advancing the understanding of fermion-boson duality in higher dimensions.

Contribution

It introduces an explicit bosonization procedure for the 3+1D Massive Thirring Model, including formulas in tensor and vector field representations, and explores mass limits.

Findings

Derived explicit bosonization formulas in 3+1D

Obtained exact bosonization of free fermions with arbitrary mass

Analyzed small and large mass limits of the bosonized theory

Abstract

We bosonize the Massive Thirring Model in 3+1D for small coupling constant and arbitrary mass. The bosonized action is explicitly obtained both in terms of a Kalb-Ramond tensor field as well as in terms of a dual vector field. An exact bosonization formula for the current is derived. The small and large mass limits of the bosonized theory are examined in both the direct and dual forms. We finally obtain the exact bosonization of the free fermion with an arbitrary mass.