The Casimir effect for parallel plates at finite temperature in the presence of one fractal extra compactified dimension

TL;DR

This paper investigates how finite temperature and a fractal extra dimension influence the Casimir effect between parallel plates, revealing that thermal effects strengthen the attractive force and that the energy remains negative at high temperatures.

Contribution

It introduces a novel analysis of the Casimir effect incorporating fractal extra dimensions and finite temperature, extending previous models to include these complex factors.

Findings

Casimir energy remains negative at high temperatures regardless of fractal dimension

Thermal effects increase the magnitude of the Casimir force

The Casimir force remains attractive under all conditions studied

Abstract

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension $\delta$ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.