Derivative expansion for the boundary interaction terms in the Casimir effect: Generalized potentials

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

PHYSICAL REVIEW D - PARTICLE AND FILDS

AMERICAN PHYSICAL SOC

Año: 2009 vol. 80 p. 850041 - 850048

0556-2821

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