Bosonization of Vector and Axial-Vector Currents in 3+1 Dimensions

TL;DR

This paper develops a bosonization method for massless fermions coupled to vector and axial-vector sources in 3+1 dimensions, incorporating anomalies and resulting in a theory with antisymmetric tensor fields.

Contribution

It introduces a novel bosonization approach in four dimensions that accounts for axial anomalies and results in a non-local tensor field theory.

Findings

Derived exact bosonization rules including axial anomaly effects

Constructed an approximate bosonized action with non-local terms

Presented a framework for bosonizing fermions with vector and axial-vector couplings

Abstract

The bosonization of a massless fermionic field coupled to both vector and axial-vector external sources is developed, following a path-integral approach. The resulting bosonized theory contains two antisymmetric tensor fields whose actions consist of non-local Kalb-Ramond-like terms plus interactions. Exact bosonization rules that take the axial anomaly for the axial current into account are derived, and an approximated bosonized action is constructed.