Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of critical exponents, of classical spin systems from single observables alone. This broadens the types of problems that the renormalization group framework can be applied to and establish universality classes of. In addition, this connection may allow for a new, data-driven way in which to find the renormalization group fixed point(s), and their relevant and irrelevant directions.

中文翻译：

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重归一化组作为Koopman运算符。

考夫曼算子理论与重归一化组直接相关。该观察结果使我们能够在不考虑平移不变性的前提下计算关键指数$\eta$ 和 $\delta$以及来自单个可观测值的经典自旋系统的临界指数比率。这拓宽了可将重归一化组框架应用于其并建立其通用性类别的问题的类型。另外，该连接可以允许以新的，数据驱动的方式来找到重归一化组固定点以及它们的相关和不相关的方向。