The Casimir Effect for Generalized Piston Geometries

TL;DR

This paper analyzes the Casimir energy and force in generalized piston geometries modeled by warped product manifolds, deriving formulas that incorporate the warping function and base manifold using zeta function regularization.

Contribution

It introduces a general framework for calculating Casimir effects in warped product piston geometries with arbitrary warping functions and base manifolds.

Findings

Formulas for Casimir energy and force involving warping function and base manifold

Application of zeta function regularization techniques

Generalized piston geometries analysis

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 $N$.