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

Abstract

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 $\delta$-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

12 pages, two figures

References in corpus (5)

• Casimir Interactions for Anisotropic Magnetodielectric Metamaterials
• Multiple Scattering Methods in Casimir Calculations
• Casimir effect with dynamical matter on thin mirrors
• Casimir energies with finite-width mirrors
• Comment on "Casimir energies with finite-width mirrors"