Casimir Energy in Non-Covariant Gauges
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The zero-point energy of a conducting spherical shell is studied by imposing the axial gauge via path-integral methods, with boundary conditions on the electromagnetic potential and ghost fields. The coupled modes are then found to be the temporal and longitudinal modes for the Maxwell field. The resulting system can be decoupled by studying a fourth-order differential equation with boundary conditions on longitudinal modes and their second derivatives. Complete agreement is found with a previous path-integral analysis in the Lorenz gauge, and with Boyer's value. This investigation leads to a better understanding of how gauge independence is achieved in quantum field theory on backgrounds with boundary.
4 pages, plain Tex, paper prepared for the QG6 parallel session on Casimir effect at 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG 9), Rome, Italy, 2-8 July 2000
4 pages, plain Tex, paper prepared for the QG6 parallel session on Casimir effect at 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG 9), Rome, Italy, 2-8 July 2000