Two-Dimensional Bosonization from Variable Shifts in the Path Integral

TL;DR

This paper introduces a novel path integral method for bosonization in (1+1)D fermionic theories, utilizing variable shifts without requiring explicit Green's functions, demonstrated on the Schwinger and Thirring models.

Contribution

It presents a new bosonization technique based solely on path integral variable shifts, avoiding reliance on Green's functions.

Findings

Successfully applied to Schwinger model

Successfully applied to massless Thirring model

Provides a Green's function independent bosonization method

Abstract

A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Greens functions. Two examples, the Schwinger model and the massless Thirring model, are worked out.