Smooth Bosonization as a Quantum Canonical Transformation

TL;DR

This paper constructs a unitary transformation in a 1+1D field theory that smoothly interpolates between the massive Thirring and sine-Gordon models, exemplifying smooth bosonization as a quantum canonical transformation.

Contribution

It introduces a continuum of equivalent theories via a unitary operator, demonstrating smooth bosonization in quantum field theory.

Findings

Unified description of Thirring and sine-Gordon models

Explicit construction of a quantum canonical transformation

Implementation of smooth bosonization in continuum field theory

Abstract

We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonization proposed by Damgaard et al. as well as an example of a quantum canonical transformation for a quantum field theory.