We discuss the formalism of Balian and Duplantier [Balian and Duplantier, Ann. Phys. (NY) 104, 300 (1977); Balian and Duplantier, Ann. Phys. (NY) 112, 165 (1978)] for the calculation of the Casimir energy for an arbitrary smooth compact surface and use it to give some examples: a finite cylinder with hemispherical caps, a torus, an ellipsoid of revolution, a cube with rounded corners and edges, and a drum made of disks and part of a torus. We propose a model function that approximately captures the shape dependence of the Casimir energy.

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Published in Physical Review A: Atomic, Molecular, and Optical Physics, v. 90, no. 1, article 012514, p. 1-8.

©2014 American Physical Society

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Funding Information

This work was supported by US AFOSR Grant No. FA9550-11-1-0297.

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