Path integral approach to bosonization of D=2 field theories

TL;DR

This paper introduces a universal path integral method for bosonizing two-dimensional quantum field theories, successfully reproducing known results and deriving new bosonic models with constraints, including connections to sigma models.

Contribution

It presents a novel path integral bosonization technique applicable to any D=2 theory, extending previous methods and deriving new constrained bosonic models.

Findings

Reproduces known results for Thirring and Schwinger models

Derives a nonlinear bosonic WZW-type theory for the Gross-Neveu model

Discusses the relation to nonlinear sigma models

Abstract

We suggest a method of bosonizing any D=2 theory. We demonstrate how it works with the examples of the Thirring and the Schwinger models, known results are reproduced. This method, being applied to the Gross-Neveu model, yields nonlinear boson WZW-type theory with additional constraint in the field space. Relation to the nonlinear sigma - model is also discussed.