Fermion Bags in the Massive Gross-Neveu Model

TL;DR

This paper investigates the formation, stability, and properties of fermion bag solutions in the massive Gross-Neveu model, revealing their time dependence, calculating their masses, and analyzing their behavior near the massless limit.

Contribution

It provides a non-perturbative analysis of fermion bags in a non-integrable 1+1D field theory, extending previous work to include mass effects and time dependence.

Findings

Fermion bags are necessarily time dependent.

Bag masses are calculated and shown to be stable.

Non-analytic behavior near the massless limit due to kink-antikink threshold.

Abstract

As has long been known, it is energetically favorable for massive fermions to deform the homogeneous vacuum around them, giving rise to extended bag-like objects. We study this phenomenon non-perturbatively in a model field theory, the $1+1$ dimensional Massive Gross-Neveu model, in the large $N$ limit. We prove that the bags in this model are necessarily time dependent. We calculate their masses variationally and demonstrate their stability. We find a non-analytic behavior in these masses as we approach the standard massless Gross-Neveu model and argue that this behavior is caused by the kink-antikink threshold. This work extends our previous work to a non-integrable field theory.