The Casimir force on a piston in the spacetime with extra compactified dimensions

Hongbo Cheng

doi:10.1016/j.physletb.2008.08.013

Abstract

A Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in high-dimensional spacetimes within the frame of Kaluza–Klein theory is analyzed. We derive and calculate the exact expression for the Casimir force on the piston. We also compute the Casimir force in the limit that one outer plate is moved to the extremely distant place to show that the reduced force is associated with the properties of additional spatial dimensions. The more dimensionality the spacetime has, the stronger the extra-dimension influence is. The Casimir force for the piston in the model including a third plate under the background with extra compactified dimensions always keeps attractive. Further we find that when the limit is taken the Casimir force between one plate and the piston will change to be the same form as the corresponding force for the standard system consisting of two parallel plates in the four-dimensional spacetimes if the ratio of the plate-piston distance and extra dimensions size is large enough.

Highlights

In 1948 a remarkable macroscopic quantum effect describing the attractive force between two conducting and neutral parallel plates was predicted by Casimir [1]
It should be pointed out that these former considerations on the topic have not involved the contribution to the vacuum energy from the area outside the confined region which depends on its dimensions while we discard the divergent terms related to the boundary depending on the geometry and dimensions during the regularization process
We prove rigorously that there must appear repulsive Casimir force between the parallel plates when the plates distance is sufficiently large in the spacetime with compatified additional dimensions, and the higher the dimensionality is, the greater the repulsive force is

Summary

Introduction

In 1948 a remarkable macroscopic quantum effect describing the attractive force between two conducting and neutral parallel plates was predicted by Casimir [1]. Since the higher-dimensional spacetime described by Kaluza-Klein theory is important and indispensable, it is crucial to discuss several models including the Casimir effect problem in this background.

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Results

Conclusion