The multiplicative and the functional renormalization group methods are applied for the four-dimensional scalar theory in Minkowski space–time. It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space–time. The parameters of the cutoff theory, defined by a subtraction point in the quasi-particle domain, are complex due to the mass-shell contributions and the renormalization group flow becomes much more involved than its Euclidean counterpart.

中文翻译：

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闵可夫斯基时空重整化

乘法和泛函重整化群方法应用于闵可夫斯基时空的四维标量理论。It is argued that the appropriate choice of the subtraction point is more important in Minkowski than in Euclidean space–time. 由准粒子域中的减法点定义的截止理论的参数由于质量壳的贡献而变得复杂，并且重整化群流变得比其欧几里得对应物更复杂。