Some developments of the Casimir effect in p-cavity of (D + 1)-dimensional space–time

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.

Four-Fermion Interaction Model on ℳD−1 ⊗ S1

“…The connection of the attractive and repulsive forces has been studied for a perfect electromagnetic conductor in [37]. Some useful formulae to calculate the Casimir force has been developed in arbitrary dimensions in [38]. In a four-fermion interaction model the sign-flip phenomenon has been found in [19,39].…”

Four-Fermion Interaction Model on $\mathcal{M}^{D-1} \otimes S^1$

“…The connection of the attractive and repulsive forces has been studied for a perfect electromagnetic conductor in [23]. Some useful formulae to calculate the Casimir force has been developed in arbitrary dimensions in [24]. In a four-fermion interaction model the sign-flip phenomenon has been found in [25].…”