Eur. Phys. J. C 25, 315-325 (2002)
A theory of the Casimir effect for compact regionsL.A. Manzoni and W.F. Wreszinski
Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 - São Paulo, S.P., Brazil
(Received: 7 March 2002 / Revised version: 12 April 2002 / Published online: 14 June 2002 )
We develop a mathematically precise framework for the Casimir effect. Our working hypothesis, verified in the case of parallel plates, is that only the regulariza tion-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.
© Società Italiana di Fisica, Springer-Verlag 2002