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arXiv · 0908.1796

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

C. D. Fosco·F. C. Lombardo·F. D. Mazzitelli
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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 $δ$-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

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C. D. Fosco, F. C. Lombardo, F. D. Mazzitelli. 2009-08-12. Derivative expansion for the boundary interaction terms in the Casimir effect: generalized $δ$-potentials. https://doi.org/10.1103/physrevd.80.085004

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