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arXiv · 1203.6522

The Casimir Effect for Generalized Piston Geometries

Guglielmo Fucci·Klaus Kirsten
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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 $N$.

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Guglielmo Fucci, Klaus Kirsten. 2012-03-29. The Casimir Effect for Generalized Piston Geometries. https://doi.org/10.1142/s0217751x12600081

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