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

References in corpus (6)

• Casimir force on a piston
• Casimir interaction of two plates inside a cylinder
• Kaluza-Klein models as pistons
• Finite Temperature Casimir Effect in Kaluza-Klein Spacetime
• Conical Casimir Pistons with Hybrid Boundary Conditions
• Spherical Casimir pistons

Cited by in corpus (1)

• Casimir Effect in the Presence of External Fields