评论“楔、锥、宇宙弦及其真空能量”
Comment on `Wedges, cones, cosmic strings and their vacuum energy'
摘要：
最近的一篇论文（2012 \emph{J. Phys.\ A} \textbf{45} 374018）通过研究圆锥及其覆盖流形（Dowker空间）的轴附近的正则化量子标量应力张量的行为来扩展。圆锥由其角度$θ_1$参数化，其中$θ_1=2π$表示平坦空间。我们发现张量分量具有$r^γ$类型的奇点，但通用前导$γ$等于${4π\over θ_1} - 2$，当且仅当$θ_1>2π$为负，当$θ_1={2π\over N}$为正整数。因此，函数在那些可以通过从平坦空间开始的图像的方法来解决的情况下是解析的，并且它们在这些情况之间插值的情况下是不发散的。由于角度为$α$的楔形体可以通过从角度为$2α$的圆锥开始的图像来求解，因此发散应力可以在具有$π<α\le 2π$的楔形体中产生，而不是在较小的楔形体中产生。
英文摘要：
A recent paper (2012 \emph{J. Phys.\ A} \textbf{45} 374018) is extended by investigating the behavior of the regularized quantum scalar stress tensor near the axes of cones and their covering manifold, the Dowker space. A cone is parametrized by its angle $θ_1$, where $θ_1=2π$ for flat space. We find that the tensor components have singularities of the type $r^γ$, but the generic leading $γ$ equals ${4π\over θ_1} - 2$, which is negative if and only if $θ_1>2π$, and is a positive integer if $θ_1={2π\over N}$. Thus the functions are analytic in those cases that can be solved by the method of images starting from flat space, and they are not divergent in the cases that interpolate between those. As a wedge of angle $α$ can be solved by images starting from a cone of angle $2α$, a divergent stress can arise in a wedge with $π<α\le 2π$ but not in a smaller one.
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