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The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force
Open AccessArticle

Casimir Energies for Isorefractive or Diaphanous Balls

by Kimball A. Milton 1,*,† and Iver Brevik 2,†
Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA
Department of Energy and Process Engineering, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2018, 10(3), 68;
Received: 1 March 2018 / Revised: 10 March 2018 / Accepted: 12 March 2018 / Published: 16 March 2018
(This article belongs to the Special Issue Casimir Physics and Applications)
It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with ε μ = 1 , a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic δ -function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented. View Full-Text
Keywords: Casimir effect; dispersion; ultraviolet divergences; infrared divergences Casimir effect; dispersion; ultraviolet divergences; infrared divergences
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Milton, K.A.; Brevik, I. Casimir Energies for Isorefractive or Diaphanous Balls. Symmetry 2018, 10, 68.

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