Casimir energy in the MIT bag model

TL;DR

This paper calculates the Casimir energy for massive Dirac fields within the MIT bag model, providing a detailed renormalization process and exact finite results for the first time, highlighting the energy's dependence on mass.

Contribution

It introduces an exact calculation of the finite, renormalized zero-point energy for massive fermionic fields in the MIT bag model, including detailed renormalization procedures.

Findings

Finite, renormalized Casimir energy obtained for massive Dirac fields.

Vacuum energy scales inversely with mass for large masses.

Detailed renormalization process distinguishes inside and outside bag configurations.

Abstract

The vacuum energies corresponding to massive Dirac fields with the boundary conditions of the MIT bag model are obtained. The calculations are done with the fields occupying the regions inside and outside the bag, separately. The renormalization procedure for each of the situations is studied in detail, in particular the differences occurring with respect to the case when the field extends over the whole space. The final result contains several constants undergoing renormalization, which can be determined only experimentally. The non-trivial finite parts which appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time, in the fermionic case. The vacuum energy behaves like inverse powers of the mass for large masses.