Next Article in Journal
Enabling Symmetric Collaboration in Public Spaces through 3D Mobile Interaction
Next Article in Special Issue
Dispersion Forces Between Fields Confined to Half Spaces
Previous Article in Journal
Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and one 7-Gonal Face
Previous Article in Special Issue
The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Symmetry 2018, 10(3), 68;

Casimir Energies for Isorefractive or Diaphanous Balls

1,†,* and 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
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
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)
Full-Text   |   PDF [397 KB, uploaded 16 March 2018]   |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Milton, K.A.; Brevik, I. Casimir Energies for Isorefractive or Diaphanous Balls. Symmetry 2018, 10, 68.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top