Functional approach to the fermionic Casimir effect

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