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A theory of the Casimir effect for compact regions

  • L.A. Manzoni
  • W.F. Wreszinski
Theoretical Physics

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.

Keywords

Exact Solution Open Problem Parallel Plate Casimir Force Asymptotic Series 
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Copyright information

© Springer-Verlag Berlin Heidelberg / Società Italiana di Fisica 2002

Authors and Affiliations

  • L.A. Manzoni
    • 1
  • W.F. Wreszinski
    • 1
  1. 1.Instituto de Física, Universidade de S ao Paulo, Caixa Postal 66318, 05315-970 - Sao Paulo, S.P., Brazil BR

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