Some Developments of the Casimir Effect in $p$-Cavity of $(D+1)$-Dimensional Spacetime

TL;DR

This paper reviews recent advances in understanding the Casimir effect in higher-dimensional rectangular cavities, including regularization methods, temperature effects, and novel configurations like the quantum spring and piston.

Contribution

It provides a comprehensive review of new developments in Casimir effect calculations for p-dimensional cavities in (D+1)-dimensional spacetime, highlighting sign determination and boundary condition effects.

Findings

Demonstration of equivalence between regularization methods

Clarification of temperature-dependent free energy regularization

Analysis of the Casimir piston configuration

Abstract

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the $p$-dimensional cavity in ($D+1$)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.