We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in D = 4 dimensions. This amounts to perturbative construction of the ϕ4 theory where the parameters of the theory are momentum-dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.

中文翻译：

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高斯不动点处的算子代数

我们考虑相关和边际标量复合算子在高斯不动点的多重乘积D = 4方面。这相当于扰动构造φ4理论参数是动量依赖源。使用精确重整化群 (ERG) 形式，我们展示了源的缩放属性如何由多个产品的短距离奇点给出。