Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $\delta$- potentials.

C. D. FOSCO, F. C. LOMBARDO, F. D. MAZZITELLI

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Año: 2009 vol. 80 p. 85004 - 85012

1550-7998

We calculate the Casimir energy for scalar fields in interaction with finite-width mirrors, described by nonlocal interaction terms. These terms, which include quantum effects due to the matter fields inside the mirrors, are approximated by means of a local expansion procedure. As a result of this expansion, an effective theory for the vacuum field emerges, which can be written in terms of generalized δ potentials. We compute explicitly the Casimir energy for these potentials and show that, for some particular cases, it is possible to reinterpret them as imposing imperfect Dirichlet boundary conditions.