Rigorous proof of attractive nature for Casimir force of p-odd hypercube

TL;DR

This paper rigorously proves that the Casimir force is attractive for massless scalar fields confined in odd-dimensional hypercubes with Dirichlet boundary conditions across various spacetime dimensions, using Epstein zeta function regularization.

Contribution

It provides a rigorous mathematical proof of the attractive nature of the Casimir force in odd-dimensional hypercubes, extending previous understanding.

Findings

Casimir force is attractive in odd-dimensional hypercubes

Proof applies to various spacetime dimensions D

Uses Epstein zeta function regularization

Abstract

The Casimir effect giving rise to an attractive force between the configuration boundaries that confine the massless scalar field is rigorously proven for odd dimensional hypercube with the Dirichlet boundary conditions and different spacetime dimensions D by the Epstein zeta function regularization.