Eur. Phys. J. C 25, 315-325 (2002)
DOI: 10.1007/s10052-002-0969-z
A theory of the Casimir effect for compact regions
L.A. Manzoni and W.F. WreszinskiInstituto 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 )
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
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
