In the paper we study the Yang–Mills effective action in the four-dimensional spacetime by using background field formalism. We give an explicit way of cutoff regularization procedure, then do a two-loop renormalization and calculate a second β-function coefficient. We also show that the two-loop singularity contains only logarithmic part in the first degree. At the same time additional properties of a Green function regular part are obtained.

中文翻译：

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4-D Yang-Mills有效作用的两环截止重新归一化

在本文中，我们使用背景场​​形式主义研究了杨-米尔斯在四维时空中的有效作用。我们给出了一种截断正则化过程的显式方法，然后进行了两环重归一化并计算了第二个β函数系数。我们还表明，二环奇点在第一阶仅包含对数部分。同时，获得了Green函数常规零件的其他属性。