Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions

Giuseppe Bimonte
Phys. Rev. D 94, 085021 – Published 21 October 2016

Abstract

Exploiting conformal symmetry, we derive a simple exact formula for the classical electromagnetic Casimir interaction of two perfectly conducting three-spheres, including the sphere-plate geometry as a special case, in four Euclidean dimensions. We verify that the short distance expansion of the Casimir energy agrees to leading order with the proximity force approximation (PFA), while the next-to-leading order is in agreement with a recently proposed derivative expansion of the Casimir energy. At the next-to-next-to-leading order we find a nonanalytic correction to PFA, which for a sphere-plate system is of the order of (d/R)3/2log(d/R), where d is the separation and R the sphere radius.

  • Figure
  • Figure
  • Received 13 July 2016

DOI:https://doi.org/10.1103/PhysRevD.94.085021

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Giuseppe Bimonte

  • Dipartimento di Fisica E. Pancini, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy and INFN Sezione di Napoli, I-80126 Napoli, Italy

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Issue

Vol. 94, Iss. 8 — 15 October 2016

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