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 ×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.