Jacobians of chiral transformations and two-dimensional bosonization

TL;DR

This paper develops a comprehensive path integral bosonization method for two-dimensional fermionic theories, applicable to both massive and massless cases, by linking the classical boson action to the Jacobian of chiral transformations.

Contribution

It introduces a complete bosonization procedure based on Jacobians of chiral transformations, extending previous approaches to a broader class of two-dimensional fermionic theories.

Findings

Successfully applied to the Schwinger model

Extended to the massive Thirring model

Generalized to non-Abelian bosonization

Abstract

We formulate a complete path integral bosonization procedure for any fermionic theory in two dimensions. The method works equally well for massive and massless fermions, and is a generalization of an approach suggested earlier by Andrianov. The classical action of the bosons in the bosonized theory is identified with -i times the logarithm of the Jacobian of a local chiral transformation, with the boson fields as transformation parameters. Three examples, the Schwinger model, the massive Thirring model and massive non-Abelian bosonization, are worked out.