Casimir Energy in a Bounded Gross-Neveu model

In this letter, we study some relevant parameters of the massless Gross-Neveu (GN) model in a finite spatial dimension for different boundary conditions. It is considered the standard homogeneousHartree-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.