Functional approach to the fermionic Casimir effect

Abstract

We use a functional approach to calculate the Casimir energy due to Dirac fields in interaction with thin, flat, parallel walls, which implement imperfect bag-like boundary conditions. These are simulated by the introduction of delta-like interactions with the walls. We show that, with a proper choice for the corresponding coupling constants, bag-model boundary condition are properly implemented. We obtain explicit expressions for the energies in 1+1 and 3+1 dimensions, for massless and massive fields.