Casimir effect with one large extra dimension

TL;DR

This paper investigates how a large extra compactified dimension affects the Casimir effect for a scalar field between plates, revealing significant deviations from standard results when the extra dimension size is comparable to the plate separation.

Contribution

It provides exact expressions for Casimir energy and pressure in the presence of a large extra dimension using ζ-function regularization, highlighting potential experimental signatures.

Findings

Casimir energy and pressure differ significantly when the extra dimension size is comparable to the plate distance.

Neumann boundary conditions yield the same results as Dirichlet in this setup.

The Casimir effect can serve as a probe for large extra dimensions.

Abstract

In this work I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet-Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the $\zeta$-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that, when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension, could be used as an effective tool to explore the existence of large compactified extra dimensions.