A theory of the Casimir effect for compact regions |
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Authors: | LA Manzoni WF Wreszinski |
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Institution: | (1) Instituto de Física, Universidade de S ao Paulo, Caixa Postal 66318, 05315-970 - Sao Paulo, S.P., Brazil , BR |
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Abstract: | We develop a mathematically precise framework for the Casimir effect. Our working hypothesis, verified in the case of parallel
plates, is that only the regularization-independent Ramanujan sum of a given asymptotic series contributes to the Casimir
pressure. As an illustration, we treat two cases: parallel plates, identifying a previous cutoff-free version (by Scharf and
Wreszinski) as a special case, and the sphere. We finally discuss the open problem of the Casimir force for the cube. We propose
an Ansatz for the exterior force and argue why it may provide the exact solution, as well as an explanation of the repulsive
sign of the force.
Received: 7 March 2002 / Revised version: 12 April 2002 / Published online: 14 June 2002 |
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