关于轨道上边界条件矩阵的对角表示

Yoshiharu Kawamura, Yasunari Nishikawa
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引用次数: 2

摘要

研究了$S^1/Z_2$和$T^2/Z_m$ ($m= 2,3,4,6 $)上边界条件矩阵的对角线表示。本文用矩阵指数表示法,给出了$S^1/Z_2$上每一类等价的边界条件矩阵对角表示的存在性的替代证明,并证明了$T^2/Z_2$、$T^2/Z_3$和$T^2/Z_4$上对角表示不一定存在。$T^2/Z_6$上的每一个等价类都有一个对角表示,因为它的边界条件是由一个单一的酉矩阵决定的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On diagonal representatives in boundary condition matrices on orbifolds
We study diagonal representatives of boundary condition matrices on the orbifolds $S^1/Z_2$ and $T^2/Z_m$ ($m=2, 3, 4, 6$). We give an alternative proof of the existence of diagonal representatives in each equivalent class of boundary condition matrices on $S^1/Z_2$, using a matrix exponential representation, and show that they do not necessarily exist on $T^2/Z_2$, $T^2/Z_3$, and $T^2/Z_4$. Each equivalence class on $T^2/Z_6$ has a diagonal representative, because its boundary conditions are determined by a single unitary matrix.
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