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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This work was supported by US AFOSR Grant No. FA9550-11-1-0297.
Straley, Joseph P. and Kolomeisky, Eugene B., "Casimir Energy of Smooth Compact Surfaces" (2014). Physics and Astronomy Faculty Publications. 285.