arXiv 0905.49282009-05-29hep-th

紧环维数$T^d_θ$的形状和$M^D\times T^d_θ$时空中的Casimir效应

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

V. K. Oikonomou

备注：: 18 pages
发表信息：: Commun.Theor.Phys.55:101-110, 2011
DOI：: 10.1088/0253-6102/55/1/20

摘要：

研究了紧致维数的形状对标量场的Casimir能量和Casimir力的影响。我们考察了有质量和无质量的标量场。总的时空拓扑是$M^D\times T^2_θ$，其中$M^D$是$D$维闵可夫斯基时空，$T^2_θ$是由$R_1$、$R_2$和$θ$描述的扭曲环面。对于$R_1=R_2$情形，我们发现当$D$ =偶数时，大质量体标量场Casimir能量是奇异的，并且这种奇异性依赖于$R$，并且在计算力时仍然是偶数。同样，无质量的卡西米尔能量和力只有在D=4（！）时才是正则的。从现象学的角度来看，这是非常有趣的。我们研究了能量和力作为$θ$的函数。我们还讨论了紧空间的稳定性问题。我们还简要讨论了一些现象学的影响。

英文摘要：

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 $M^D\times T^2_θ$, 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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英文摘要：

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