Casimir Effect with a Helix Torus Boundary Condition

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_c 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_c 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 c^' and the pressure is independent of the mass at r = r c^' in the D = 3 case.