Casimir Energy in a Bounded Gross-Neveu model

We study the Casimir energy and forces associated with the vacuum of the massless Gross-Neveu (GN) model in a finite spatial dimension for different boundary conditions. The standard solution given by the Hartree-Fock method is considered using the generalized method of the zeta function, with the aim of studying the dynamic generation of mass and the associated beta function. It is found that the beta function does not depend on the boundary conditions. Then, considering several boundary conditions, the corresponding Casimir energies and forces were obtained. We obtain that the nature of the forces depends as much on the type of contour condition as on the magnitude of the space.