Paper detail

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

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 $ξ^2=(ε_1-ε_2)^2/ (ε_1+ε_2)^-2 = (μ_1-μ_2)^2/(μ_1+ μ_2)^2 \le 1$ is used, where $ε_1$ and $μ_1$ are, respectively, the permittivity and permeability of the material making up the cylinder and $ε_2$ and $μ_2$ 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 $ξ^4$. The explicit formulas permitting us to find numerically the Casimir energy for any fixed value of $ξ^2$ 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.