Generalized Abel-Plana formula as a renormalization tool in quantum field theory with boundaries

Abstract

We apply the generalized Abel-Plana formula for the investigation of one-loop quantum effects on manifolds with boundaries. This allows to extract from the vacuum expectation values of local physical observables the parts corresponding to the geometry without boundaries and to present the boundary-induced parts in terms of integrals strongly convergent for the points away from the boundaries. As a result, the renormalization procedure for these observables is reduced to the corresponding procedure for the bulks without boundaries.