Electromagnetic semitransparent δ -function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a delta -function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting delta -function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness d with plasma frequency (ProQuest: Formulae and/or non-USASCII text omitted) = [zeta] sub(p)/d reduces to a delta -function plate for frequencies ( omega = i[zeta] satisfying [zeta]d