# Casimir Energy in a Bounded Gross-Neveu model

## TL;DR

This paper investigates the Casimir effect and dynamical mass generation in the massless Gross-Neveu model with finite boundaries, revealing boundary condition independence of the beta function and complex force behaviors.

## Contribution

It provides a detailed analysis of the Casimir energy and beta function in a bounded Gross-Neveu model, highlighting boundary condition effects on physical parameters.

## Key findings

- Beta function is independent of boundary conditions.
- Casimir forces can be attractive or repulsive depending on parameters.
- Massless Gross-Neveu model exhibits complex boundary-dependent behaviors.

## Abstract

In this letter we study some relevant physical parameters of the massless Gross-Neveu model in a finite spatial dimension for different boundary conditions. It is considered the standard homogeneous Hartree Fock solution using zeta function regularization for the study the mass dynamically generated and its respective beta function. It is found that the beta function does not depend on the Boundary conditions. On the other hand, it was considered the Casimir effect of the resulting effective theory. There appears a complex picture where the sign of the generated forces depends on the parameters used in the study.