VECTOR CASIMIR EFFECT FOR A D-DIMENSIONAL SPHERE

The Casimir energy or stress due to modes in a D-dimensional volume su bject to TM (mixed) boundary conditions on a bounding spherical surfac e is calculated. Both interior and exterior modes are included. Togeth er with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ''electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensi ons, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularit ies) occur for integer dimensions D less than or equal to 1. Particula r attention is given the interesting case of D = 2.