The Shape of Compact Toroidal Dimensions $T^d_θ$ and the Casimir Effect on $M^D\times T^d_θ$ spacetime

V. K. Oikonomou

doi:10.1088/0253-6102/55/1/20

paper

The Shape of Compact Toroidal Dimensions $T_{θ}^{d}$ and the Casimir Effect on $M^{D} \times T_{θ}^{d}$ spacetime

arXiv:0905.4928 · doi:10.1088/0253-6102/55/1/20

Abstract

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 $M^{D} \times T_{θ}^{2}$ , where $M^{D}$ is the $D$ dimensional Minkowski spacetime and $T_{θ}^{2}$ 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.

18 pages

The Shape of Compact Toroidal Dimensions $T_{θ}^{d}$ and the Casimir Effect on $M^{D} \times T_{θ}^{d}$ spacetime

Abstract

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Cited by in corpus (3)

The Shape of Compact Toroidal Dimensions $T_{θ}^{d}$ and the Casimir Effect on $M^{D} \times T_{θ}^{d}$ spacetime