Bosonic Structure of a 2-Dimensional Fermion Model with Interaction among Different Species II -- N-species Case --

TL;DR

This paper extends a 2D fermion model with multiple species to N species, deriving its bosonic equivalent and analyzing the conditions for physical sensibility and field reduction.

Contribution

It generalizes a previous two-species model to N species, revealing how coupling constants influence the bosonic representation and field content.

Findings

Coupling constants must be in specific regions for physical validity.

Certain boson fields vanish at specific coupling values.

The N-species fermion model reduces to fewer boson fields under certain conditions.

Abstract

We study a massive Thirring-like model in 2-dimensional space-time, which contains fermions with arbitrary number (N) of different species. This model is an extension of that of a previous paper, where we have considered two-species case. By this extension we expect that we can expose more general structures of this kind of model. We obtain the equivalent boson model with N species to our fermion model. We find that the coupling constant must be set in some regions in order for the model to be physically sensible. It seems hard to find such regions from direct obsavation of the original fermion model. We also find that for specific values of the coupling constant some of the boson fields disappear from the system. Therefore, the N-species fermion model is described by the boson model with fewer species.