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arXiv · 2212.04733

Casimir self-energy of a \delta-\delta' sphere

C. Romaniega·J. M. Munoz-Castaneda·I. Cavero-Pelaez
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Abstract

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called "delta-delta prime" interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions.

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C. Romaniega, J. M. Munoz-Castaneda, I. Cavero-Pelaez. 2022-12-09. Casimir self-energy of a \delta-\delta' sphere. https://doi.org/10.1103/physrevd.107.025002

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