Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Kimball A. Milton, A. V. Nesterenko, and V. V. Nesterenko
Phys. Rev. D 59, 105009 – Published 14 April 1999
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Abstract

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder (ɛ1,μ1) and of that which makes up the surroundings (ɛ2,μ2) obey the relation ɛ1μ1=ɛ2μ2. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric-diamagnetic cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in a complete agreement with that obtained by DeRaad and Milton who employed a Green’s function technique with an ultraviolet regulator.

  • Received 19 October 1998

DOI:https://doi.org/10.1103/PhysRevD.59.105009

©1999 American Physical Society

Authors & Affiliations

Kimball A. Milton*

  • Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019

A. V. Nesterenko

  • Physical Department, Moscow State University, Moscow, 119 899, Russia

V. V. Nesterenko

  • Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia

  • *Electronic address: milton@mail.nhn.ou.edu
  • Electronic address: nestr@thsun1.jinr.ru

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Vol. 59, Iss. 10 — 15 May 1999

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