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THE CASIMIR EFFECT FOR GENERALIZED PISTON GEOMETRIES

GUGLIELMO FUCCI

Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA

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and

KLAUS KIRSTEN

Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX 76798-7328, USA

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https://doi.org/10.1142/S0217751X12600081Cited by:7 (Source: Crossref)

Abstract

In this paper we study the Casimir energy and force for generalized pistons constructed from warped product manifolds of the type I ×_f N where I = [a, b] is an interval of the real line and N is a smooth compact Riemannian manifold either with or without boundary. The piston geometry is obtained by dividing the warped product manifold into two regions separated by the cross section positioned at R ∈ (a, b). By exploiting zeta function regularization techniques we provide formulas for the Casimir energy and force involving the arbitrary warping function f and base manifold N.

Keywords:

PACS: 11.10.Kk, 02.40.Ky

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