Bosonic Structure of a 2-Dimensional Fermion Model with Interaction among Different Speices

TL;DR

This paper explores a two-species fermion model in 2D, deriving a bosonic equivalent via bosonization, revealing unique operator correspondences and a special coupling case where the model simplifies to a single Sine-Gordon field.

Contribution

It extends bosonization to a two-species fermion model with inter-species interaction, providing new operator correspondences and identifying a special coupling case simplifying the model.

Findings

One boson becomes free at a specific coupling.

The other boson corresponds to a Sine-Gordon field.

Model reduces to a single Sine-Gordon model at a special coupling.

Abstract

We study a massive Thirring-like model in 2-dimensional space-time, which contains two different species of fermions. This model is a field theoretical version of the quantum mechanical model originally proposed by Gl\"{o}ckle, Nogami and Fukui, where different fermions interact with each other through $\delta$-function potentials. We derive a corresponding boson model by the bosonization technique in the path integral formulation. This is a simple but non-trivial extension of the freedom of the bosonization technique. Operator correspondences between fermion and boson fields are given. One of these could not be realistically expected from the naive correspondence of the original single-species models. It is essential for this point that in our model fermions of the same kind do not interact with each other directly. We find that for a specific value of the coupling constant, one boson field becomes free while the other is a Sine-Gordon field. For this case, therefore, our two-species model is equivalent to the ordinary Sine-Gordon model of a single boson field.