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 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 [Formula: see text] and the pressure is independent of the mass at [Formula: see text] in the D = 3 case.
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