Conical Casimir Pistons with Hybrid Boundary Conditions

TL;DR

This paper calculates the Casimir energy and force for massless scalar fields with hybrid boundary conditions in a generalized cone, providing explicit formulas in various dimensions using spectral zeta function regularization.

Contribution

It introduces a method to compute Casimir effects with hybrid boundary conditions in generalized cones, including explicit results for specific dimensions.

Findings

Explicit formulas for Casimir energy and force in arbitrary dimensions.

Specialized results for a spherical piston in dimensions 2 to 5.

Demonstrates the use of spectral zeta function regularization in this context.

Abstract

In this paper we compute the Casimir energy and force for massless scalar fields endowed with hybrid boundary conditions, in the setting of the bounded generalized cone. By using spectral zeta function regularization methods, we obtain explicit expressions for the Casimir energy and force in arbitrary dimensions in terms of the zeta function defined on the piston. Our general formulas are, subsequently, specialized to the case in which the piston is modelled by a $d$-dimensional sphere. In this particular situation, explicit results are given for $d=2,3,4,5$.