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The Casimir effect for conical pistons

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Abstract

In this paper we utilize ζ-function regularization techniques in order to compute the Casimir force for massless scalar fields subject to Dirichlet and Neumann boundary conditions in the setting of the conical piston. The piston geometry is obtained by dividing the bounded generalized cone into two regions separated by its cross section positioned at a with a ∈ (0, b) with b > 0. We obtain expressions for the Casimir force that are valid in any dimension for both Dirichlet and Neumann boundary conditions in terms of the spectral ζ-function of the piston. As a particular case, we specify the piston to be a d-dimensional sphere and present explicit results for d = 2, 3, 4, 5.

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Authors and Affiliations

  1. Department of Mathematics, Baylor University, One Bear Place # 97328, Waco, TX, 76798, U.S.A.

    Guglielmo Fucci & Klaus Kirsten

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  1. Guglielmo Fucci
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  2. Klaus Kirsten
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Correspondence to Klaus Kirsten.

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ArXiv ePrint: 1101.5409

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Fucci, G., Kirsten, K. The Casimir effect for conical pistons. J. High Energ. Phys. 2011, 16 (2011). https://doi.org/10.1007/JHEP03(2011)016

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