Comments on Bosonization of the extended Thirring Model with SU(2) Symmetry

TL;DR

This paper critically examines the bosonization process of the extended Thirring model with SU(2) symmetry, highlighting challenges and misconceptions related to fermion determinant calculation and ghost fields.

Contribution

It clarifies the difficulties in bosonizing the model correctly, especially concerning the fermion determinant and ghost fields, challenging previous simplified views.

Findings

Bosonization of the model is complex due to fermion determinant issues.

Decoupling transformation may introduce ghost fields, complicating the bosonization.

Contradicts simplified textbook explanations of the process.

Abstract

Bosonization of the extended Thirring model with SU(2) symmetry in the Minkowski path integral method is discussed. We argue that it is not an easy task to bosonize such a model if we derive correctly the fermion determinant which is induced with the decoupling transformation because it seems that there arise ghost fields. This is contrary to what is shown in a textbook and some people believe.