Vacuum energy in the presence of dielectric and conducting surfaces

The polarization of the electromagnetic vacuum is examined in the neighborhood of dielectric and conducting surfaces and the energy associated with this polarization is shown to depend on a cutoff related to the microstructure of the boundary. The appearance of the cutoff permits the vacuum energy to be expressed in terms of a surface tension and certain higher shape tensions. For the case of a dielectric boundary the surface tension reproduces the Schmitt-Lucas formula which accounts reasonably for the observed surface tensions of many materials. The curvature tension is also calculated and it seems the effect of this energy may well be accessible to experimental verification. For the case of perfectly conducting surfaces the first four shape tensions are calculated. It is shown that previous calculations of the vacuum energy due to perfectly conducting surfaces are in error and these errors are corrected.