Graphical functions are special position space Feynman integrals, which can be used to calculate Feynman periods and one- or two-scale processes at high loop orders. With graphical functions, renormalization constants have been calculated to loop orders seven and eight in four-dimensional $\phi^4$ theory and to order five in six-dimensional $\phi^3$ theory. In this article we present the theory of graphical functions in even dimensions $\geq 4$ with detailed reviews of known properties and full proofs whenever possible.

中文翻译：

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偶数维图形函数

图形函数是特殊的位置空间费曼积分，可用于计算费曼周期和高环阶的一或二尺度过程。使用图形函数，已经计算出重整化常数以循环四维 $\phi^4$ 理论中的七阶和八阶，以及六维 $\phi^3$ 理论中的五阶。在本文中，我们将介绍偶数维 $\geq 4$ 中的图函数理论，并尽可能详细地回顾已知属性和完整证明。