Vector Casimir effect for a-dimensional sphere
- 15 April 1997
- journal article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 55 (8) , 4940-4946
- https://doi.org/10.1103/physrevd.55.4940
Abstract
The Casimir energy or stress due to modes in a D-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together 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 dimensions, 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 singularities) occur for integer dimensions $D\le1$. Particular attention is given the interesting case of D=2.
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