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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
()-dimensional spacetime.
We obtain the exact results of the Casimir energy density and pressure for
any 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 of
the ratio of the lengths at which the pressure vanishes. The pressure
changes from negative to positive as the ratio passes through
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 and the pressure is
independent of the mass at in the D=3 case.Comment: 11 pages, 3 figures, to be published in Mod. Phys. Lett.
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