The Casimir Effect for Generalized Piston Geometries

Abstract

In this paper we study the Casimir energy and force for generalized pistons constructed from warped product manifolds of the type $I{\times }_{f}N$ 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 $R\in (a,b)$. By exploiting zeta function regularization techniques we provide formulas for the Casimir energy and force involving the arbitrary warping function $f$ and base manifold $N$.

16 pages, LaTeX. To appear in the proceedings of the Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT11). Benasque, Spain, September 18-24, 2011

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• Casimir pistons with generalized boundary conditions: a step forward
• The Casimir Effect for Thick Pistons