The Shape of Compact Toroidal Dimensions T d θ and the Casimir Effect on M D × T d θ spacetime
نویسنده
چکیده
We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is M D ×T 2 θ , where M D is the D dimensional Minkowski spacetime and T 2 θ the twisted torus described by R 1 , R 2 and θ. For the case R 1 = R 2 we found that the massive bulk scalar field Casimir energy is singular for D=even and this singularity is R-dependent and remains even when the force is calculated. Also the massless Casimir energy and force is regular only for D = 4 (!). This is very interesting phenomenologically. We examine the energy and force as a function of θ. Also we address the stabilization problem of the compact space. We also briefly discuss some phenomenological implications.
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