The Gross-Neveu model on the light cone

TL;DR

This paper analyzes the massive Gross-Neveu model using light cone quantization, revealing a trivial vacuum, issues at zero mass, and the emergence of the running coupling as a normal ordering effect.

Contribution

It provides an explicit solution of constraints in the light cone framework and discusses the vacuum structure and coupling emergence in the model.

Findings

Vacuum is trivial in the massive case

Quantization fails at zero mass

Running coupling emerges from normal ordering

Abstract

We consider the (massive) Gross-Neveu model using the light cone quantization where we solve the constraints explicitly. We show that the vacuum is trivial and that the quantization fails when $m=0$. We discuss how the running coupling constant emerges as a pure normal ordering effect in this context and the bound state equation.