Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus
Some twisted self-dual solutions for the Yang-Mills equations on a hypertorus
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超圆环上杨-米尔斯方程的一些扭曲自对偶解
DOI：
10.1007/bf01208900
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发表时间：
1981
影响因子：
2.4
通讯作者：
G. Hooft
中科院分区：
文献类型：
--
作者：
G. Hooft
SU(N) Yang-Mills 方程在具有周期性边界条件（上环）的四维欧几里得盒中考虑。可以在这些边界条件中引入规范不变的扭曲，用整数 nμν(= −nμν) 标记，定义为模 N。该空间中的庞特里亚金数通常是分数。每当这个数字为零时，方程 Gμν=0 就有解 这里 Gμν 是协变旋度。当这个数字不为零时，我们找到方程的一组解，前提是盒子的周期aμ满足某些关系。
TheSU(N) Yang-Mills equations are considered in a four-dimensional Euclidean box with periodic boundary conditions (hypertorus). Gauge-invariant twists can be introduced in these boundary conditions, to be labeled with integersnμν(= −nμν), defined moduloN. The Pontryagin number in this space is often fractional. Whenever this number is zero there are solutions to the equationsGμν=0 HereGμνis the covariant curl. When this number is not zero we find a set of solutions to the equations, provided that the periodsaμof the box satisfy certain relations.