A new view of the procedure of renormalizations in nonrenormalizable theories is proposed. This view is based on the standard procedure of the BPHZ R-operation, which is equally applicable to any local quantum field theory irrespective of renormalizability. The key point is that the multiplicative renormalization used in renormalizable theories is replaced by an operation in which the renormalization constant depends on the momenta over which integration in subgraphs is performed. In this case, the requirement for the counterterms to be local (precisely as in renormalizable theories) leads to recurrence relations between leading, subleading, etc., ultraviolet divergences in all orders of perturbation theory. This allows one to obtain generalized renormalization group equations for scattering amplitudes, which have an integro-differential form and lead to the summation of the leading asymptotics, just as in renormalizable theories.

中文翻译：

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关于不可重整化理论中的重整化

提出了不可重整化理论中重整化过程的新观点。该视图基于BPHZ R的标准程序-运算，与重新规范化无关，同样适用于任何局部量子场论。关键点在于，可重归一化理论中使用的乘法可重归一化被操作替换，其中重归一化常数取决于子图中进行积分的时刻。在这种情况下，对反项必须是局部的（确切地说是在可重归一化的理论中）导致在所有扰动理论的先导，次导等紫外线散度之间的重复关系。就像重归一化的理论一样，这使人们可以获得用于散射幅度的广义重归一化组方程，该方程具有整数微分形式并导致前渐近性的求和。