On bosonization in $3$ dimensions

TL;DR

This paper extends a path-integral bosonization scheme in 3D by incorporating full momentum dependence, unifying the treatment of massive and massless fermions and aligning with canonical quantization results for massless cases.

Contribution

It introduces a comprehensive bosonization approach in 3D that accounts for momentum dependence, bridging massive and massless fermion cases and reconciling different quantization methods.

Findings

Unified treatment of massive and massless fermions in 3D bosonization.

Results for massless fermions match canonical quantization approaches.

Enhanced understanding of fermion-boson duality in three dimensions.

Abstract

A recently proposed path-integral bosonization scheme for massive fermions in $3$ dimensions is extended by keeping the full momentum-dependence of the one-loop vacuum polarization tensor. This makes it possible to discuss both the massive and massless fermion cases on an equal footing, and moreover the results it yields for massless fermions are consistent with the ones of another, seemingly different, canonical quantization approach to the problem of bosonization for a massless fermionic field in $3$ dimensions.