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

Details Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $δ$-potentials Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $δ$-potentials

2009-08-12

arxiv.org/abs/0908.1796v1

Phys.Rev.D80:085004,2009

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, two figures

Scientific paper

10.1103/PhysRevD.80.085004

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

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