Exact Casimir energies at nonzero temperature: Validity of proximity force approximation and interaction of semitransparent spheres

Abstract

In this paper, dedicated to the career of Tom Erber, we consider the Casimir interaction between weakly coupled bodies at nonzero temperature. For the case of semitransparent bodies, that is, ones described by delta-function potentials, we first examine the interaction between an infinite plane and an arbitrary curved surface. In weak coupling, such an interaction energy coincides with the exact form of the proximity force approximation obtained by summing the interaction between opposite surface elements at arbitrary temperature. This result generalizes a theorem proved recently by Decca et al. We also obtain exact closed-form results for the Casimir energy at arbitrary temperature for weakly coupled semitransparent spheres.

7 pages, 1 eps figure. Invited paper for the Festschrift for Tom Erber. This version corrects a misstatement about the order of the polynomial in the Appendix.

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