Casimir energy of smooth compact surfaces

Abstract

We discuss the formalism of Balian and Duplantier 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, the torus, 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 which approximately captures the shape dependence of the Casimir energy.