Casimir energy of a compact cylinder under the condition $εμ= c^{-2}$

Details Casimir energy of a compact cylinder under the condition $εμ= c^{-2}$ Casimir energy of a compact cylinder under the condition $εμ= c^{-2}$

1999-07-27

arxiv.org/abs/hep-th/9907192v3

Phys.Rev. D60 (1999) 125007

Physics

High Energy Physics

High Energy Physics - Theory

REVTeX, 12 pages, 1 figure in a separate fig1.eps file, 1 table; minor corrections in English and misprints; version to be pub

Scientific paper

10.1103/PhysRevD.60.125007

The Casimir energy of an infinite compact cylinder placed in a uniform unbounded medium is investigated under the continuity condition for the light velocity when crossing the interface. As a characteristic parameter in the problem the ratio $\xi^2=(\epsilon_1-\epsilon_2)^2/ (\epsilon_1+\epsilon_2)^-2 = (\mu_1-\mu_2)^2/(\mu_1+ \mu_2)^2 \le 1$ is used, where $\epsilon_1$ and $\mu_1$ are, respectively, the permittivity and permeability of the material making up the cylinder and $\epsilon_2$ and $\mu_2$ are those for the surrounding medium. It is shown that the expansion of the Casimir energy in powers of this parameter begins with the term proportional to $\xi^4$. The explicit formulas permitting us to find numerically the Casimir energy for any fixed value of $\xi^2$ are obtained. Unlike a compact ball with the same properties of the materials, the Casimir forces in the problem under consideration are attractive. The implication of the calculated Casimir energy in the flux tube model of confinement is briefly discussed.

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