Casimir effect with a helix torus boundary condition

TL;DR

This paper calculates the Casimir energy and pressure for a scalar field with a helix torus boundary condition in higher-dimensional spacetime, revealing how topology and size ratios influence quantum vacuum effects.

Contribution

It provides exact formulas for Casimir energy and pressure in arbitrary dimensions with helix torus topology, including mass effects and critical size ratios.

Findings

Pressure changes sign at a critical size ratio r_{crit}.

Pressure approaches massless field results as mass approaches zero.

In D=3, pressure is independent of mass at a specific ratio r_{crit}^{}.

Abstract

We use the generalized Chowla-Selberg formula to consider the Casimir effect of a scalar field with a helix torus boundary condition in the flat ($D+1$)-dimensional spacetime. We obtain the exact results of the Casimir energy density and pressure for any $D$ for both massless and massive scalar fields. The numerical calculation indicates that once the topology of spacetime is fixed, the ratio of the sizes of the helix will be a decisive factor. There is a critical value $r_{crit}$ of the ratio $r$ of the lengths at which the pressure vanishes. The pressure changes from negative to positive as the ratio $r$ passes through $r_{crit}$ increasingly. In the massive case, we find the pressure tends to the result of massless field when the mass approaches zero. Furthermore, there is another critical ratio of the lengths $r_{crit}^{\prime}$ and the pressure is independent of the mass at $r=r_{crit}^{\prime}$ in the D=3 case.