In this paper, we discuss the interaction of non-Abelian SU(2) Yang–Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang–Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show ‘beat patterns’ and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang–Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang–Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang–Mills coupling constant. In a cosmological background, the Yang–Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang–Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time.

在本文中，我们讨论非阿贝尔SU(2)杨-米尔斯行进波与引力波的相互作用。我们求解并获得了不同背景下的纯杨-米尔斯方程的一些有趣的解，以及由引力波引起的微扰解。这些扰动显示出“节拍模式”，并且根据边界条件，频率发生变化。在平坦时空中，当杨-米尔斯场和引力波处于同一方向时，不存在相互作用，除非杨-米尔斯场存在自相互作用。在具有非零自相互作用的系统中，扰动的幅度与杨-米尔斯耦合常数成反比。在宇宙学背景下，即使没有杨米尔斯渐进场的自相互作用，杨米尔斯场和引力波在同一方向时也会相互作用。我们发现，在规范场的电弱对称破缺相中，相互作用仅在无穷小的时间内是微扰的。