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

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.