On a theory of the Casimir effect |
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| Institution: | 1. Departamento de Física Teórica, Atómica y Óptica and IMUVA Universidad de Valladolid, Paseo Belén 7, Valladolid 47011, Spain;2. Laboratoire de Mathématique et Physique Théorique, CNRS UMR 7350, Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont 37200 Tours, France;3. Departamento de Física, FCEIA, UNR, Av. Pellegini 250, Rosario 2000, Argentina |
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| Abstract: | We develop a mathematically precise framework for the Casimir effect. A major role is played by Dietz's idea of identifying the Casimir energy as the regularization-independent Ramanujan sum of an asymptotic series. As an illustration, we treat two cases: parallel plates 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. |
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