Finite Casimir Effect in Quantum Field Theory

The computation of the Casimir effect is directly linked to the modification of the vacuum energy due to the presence of boundaries. In order to have complete control of the short distance behavior also near the boundary, the analysis is performed in the precise framework of a local, renormalizable quantum field theory which includes the boundary contributions. We show that the presence of soft terms at the boundary, needed to implement Robin's conditions, introduces a free parameter in the final, finite answer, a parameter which has no natural normalization condition within the scheme. We discuss in detail a free massless scalar field in R₃ with plane and cylindric boundaries; in particular the second case, where the boundary soft term is essential to remove sub-leading short distance divergencies, suffers the mentioned indeterminacy, which might be removed by a phenomenological interpretation relating the soft term to a microscopic description of the boundary.