The generalized Gross-Neveu model on the light cone

TL;DR

This paper studies the generalized Gross-Neveu model using discretized light cone quantization, revealing a non-trivial vacuum in the bare theory but a trivial vacuum after renormalization, with finite Bethe-Salpeter equations.

Contribution

It demonstrates the vacuum structure of the generalized Gross-Neveu model and derives finite Bethe-Salpeter equations within this framework.

Findings

Bare theory vacuum is non-trivial with vector current coupling.

Renormalized theory has a trivial vacuum.

Bethe-Salpeter equations are finite and complete.

Abstract

We investigate the generalized Gross-Neveu model using the discretized light cone quantization and we find that the vacuum of the bare theory is {\sl non} trivial in presence of vectorial current coupling when the simplest and most natural form of quantum constraints is used. Nevertheless the vacuum of the renormalized theory is trivial. In the thermodynamic the Bethe-Salpiter equations which are obtained contain all the terms needed to make them finite.