Different Approaches for Bosonization in Higher Dimensions

TL;DR

This paper compares two methods of bosonization in higher dimensions, demonstrating their equivalence and applying them to the Massive Thirring Model in 3D and 4D, with exact results for free fermions.

Contribution

It introduces and compares two distinct bosonization approaches in higher dimensions, establishing their equivalence and extending the analysis to arbitrary dimensions.

Findings

Both approaches yield equivalent bosonized Lagrangians and currents.

Exact results are obtained for free massive fermion theories.

The methods are applied successfully to the Massive Thirring Model in 3D and 4D.

Abstract

We describe two distinct approaches for bosonization in higher dimensions; one is based on a direct comparison of current correlation functions while the other relies on a Master lagrangean formalism. These are used to bosonise the Massive Thirring Model in three and four dimensions in the weak coupling regime but with an arbitrary fermion mass. In both approaches the explicit bosonised lagrangean and current are derived in terms of gauge fields. The complete equivalence of the two bosonization methods is established. Exact results for the free massive fermion theory are also obtained. Finally, the two-dimensional theory is revisited and the possibility of extending this analysis for arbitrary dimensions is indicated.