We propose a systematic way of finding solutions to classical Yang-Mills equation with non-trivial topology. This approach is based on one of Wightman axioms for quantum field theory, which is referred to as form invariance condition in this letter. For a given gauge group and a spacetime with certain isometries, thanks to this axiom that imposes strong constraints on the general Ansatz, a systematic way of solving Yang-Mills equation can be obtained in both flat and curved spacetimes. In order to demonstrate this method, we recover various known solutions as special cases as well as produce new solutions not previously reported in the literature.

中文翻译：

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寻找杨-米尔斯方程解的拓扑方法

我们提出了一种用非平凡拓扑找到经典杨-米尔斯方程解的系统方法。这种方法基于量子场论的 Wightman 公理之一，在这封信中称为形式不变条件。对于给定的规范群和具有某些等距的时空，由于这个公理对一般 Ansatz 强加了强约束，因此可以在平坦和弯曲的时空中获得解杨米尔斯方程的系统方法。为了演示这种方法，我们恢复了各种已知的解决方案作为特殊情况，并产生了以前没有在文献中报道过的新解决方案。