The flow equations of the renormalization group allow one to analyze the perturbative n-point functions of renormalizable quantum field theories. Rigorous bounds implying renormalizability permit one to control large momentum behavior, infrared singularities, and large order behavior in a number of loops and a number of arguments n. In this paper, we analyze the Euclidean four-dimensional massive ϕ4 theory using lattice regularization. We present a rigorous proof that this quantum field theory is renormalizable to all orders of the loop expansion based on the flow equations. The lattice regularization is known to break Euclidean symmetry. Our main result is the proof of the restoration of rotation and translation invariance in the renormalized theory using flow equations.

中文翻译：

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用流动方程对晶格正则化 ϕ44 进行微扰重整化

重整化群的流动方程允许人们分析可重整化量子场论的微扰 n 点函数。意味着可重整化的严格界限允许人们在多个循环和多个参数 n 中控制大动量行为、红外奇点和大阶行为。在本文中，我们使用格子正则化来分析欧几里得四维大规模 ϕ4 理论。我们提出了一个严格的证明，即基于流动方程，该量子场论可重整化为环展开的所有阶次。已知晶格正则化会破坏欧几里得对称性。我们的主要结果是使用流动方程证明了重整化理论中旋转和平移不变性的恢复。