Ground state energy for a penetrable sphere and for a dielectric ball

1998/11/02 by M. Bordag, Klaus Kirsten, K. Kirsten +2 · 9 citations
Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #hep-th

paper · pdf · doi:10.1103/physrevd.59.085011

published as Phys.Rev.D59:085011,1999 · 18 pages, 1 figure, subm. to Phys. Rev. D

arxiv created 1998/11/02 · openalex publication_date 1999/03/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We analyze the ultraviolet divergences in the ground state energy for a penetrable sphere and a dielectric ball. We argue that for massless fields subtraction of the ``empty space'' or the ``unbounded medium'' contribution is not enough to make the ground state energy finite whenever the heat kernel coefficient a₂ is not zero. It turns out that a₂\ensuremath≠0 for a penetrable sphere, a general dielectric background, and the dielectric ball. To our surprise, for more singular configurations, as in the presence of sharp boundaries, the heat kernel coefficients behave to some extent better than in the corresponding smooth cases, making, for instance, the dilute dielectric ball a well-defined problem.

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