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

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.

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19 pages, 2 figures

energy: Casimir
expansion: derivative
symmetry: conformal
electromagnetic
Euclidean
geometry
sphere

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