Spherical Universe topology and the Casimir effect
Spherical Universe topology and the Casimir effect
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球形宇宙拓扑和卡西米尔效应
DOI：
10.1088/0264-9381/21/17/012
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发表时间：
2004
影响因子：
3.5
通讯作者：
J. S. Dowker
中科院分区：
文献类型：
--
作者：
J. S. Dowker
最近对宇宙可能的非平凡拓扑的兴趣，以及由此产生的拉普拉斯本征问题的分析，促使我们重新进行了一段时间前的计算。本文重新讨论了无不动点因式化3-球S3/Γ上的模问题，并将其应用于自旋为0，1/2和1的无质量场的场论计算。特别是因子（包括透镜空间）的退化，以几何方式更整齐地重新推导。同样，真空能量重新评估的一种改进的技术，并表示在多面体不变的多项式次数，因此，有效的所有情况下，没有角度替代。另一个等价的表达式是利用Γ的循环分解给出的。还确定了标量函数行列式。作为奖励，光谱不对称函数η（s）用相同的方法处理，并给出了单侧透镜空间上η（− 2 n）的显式形式。
Recent interest in the possible non-trivial topology of the Universe, and the resulting analysis of the Laplacian eigenproblem, has prompted a reprise of calculations done by ourselves some time ago. The mode problem on the fixed-point-free factored 3-sphere, S3/Γ, is re-addressed and applied to some field theory calculations for massless fields of spin 0, 1/2 and 1. In particular the degeneracies on the factors, including lens spaces, are rederived more neatly in a geometric fashion. Likewise, the vacuum energies are re-evaluated by an improved technique and expressed in terms of the polyhedrally invariant polynomial degrees, being thus valid for all cases without angle substitution. An alternative, but equivalent expression is given employing the cyclic decomposition of Γ. The scalar functional determinants are also determined. As a bonus, the spectral asymmetry function, η(s) is treated by the same approach and explicit forms are given for η(−2n) on one-sided lens spaces.