Casimir Pistons with General Boundary Conditions

TL;DR

This paper investigates the Casimir energy and force in a higher-dimensional piston setup with general boundary conditions, using spectral zeta function regularization, and provides explicit formulas depending on the manifold's spectral properties.

Contribution

It introduces a comprehensive analysis of Casimir effects with arbitrary boundary conditions in higher-dimensional pistons, extending previous models with new spectral techniques.

Findings

Derived explicit formulas for Casimir energy and force with general boundary conditions.

Showed dependence of Casimir effects on the spectral zeta function of the manifold.

Specialized results to the case of a spherical manifold.

Abstract

In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product $I\times N$, with $I=[0,L]\subset\mathbb{R}$ and $N$ a smooth, compact Riemannian manifold with or without boundary. The study of the Casimir energy and force for this configuration is performed by employing the spectral zeta function regularization technique. The obtained analytic results depend explicitly on the spectral zeta function associated with the manifold $N$ and the parameters describing the general boundary conditions imposed. These results are then specialized to the case in which the manifold $N$ is a $d$-dimensional sphere.