论文标题
Feynman时期的递归计算
Recursive computation of Feynman periods
论文作者
论文摘要
Feynman时期是Feynman的积分，不依赖外部运动学。它们的计算是量子场理论的许多应用所必需的，它通过图形函数或等效的共形四点积分极大地促进了它们。我们描述了一组转换规则，这些规则对此类功能作用，并允许其递归计算在任意的范围内。作为一个具体的示例，我们在$ ϕ^3 $理论中计算所有无副段的Feynman时期，最高六个循环和607 Feynman时期的561个循环。我们的结果支持了量子场理论中的coaction结构的猜想，并表明$ ϕ^3 $和$ ϕ^4 $理论共享相同的数字内容。
Feynman periods are Feynman integrals that do not depend on external kinematics. Their computation, which is necessary for many applications of quantum field theory, is greatly facilitated by graphical functions or the equivalent conformal four-point integrals. We describe a set of transformation rules that act on such functions and allow their recursive computation in arbitrary even dimensions. As a concrete example we compute all subdivergence-free Feynman periods in $ϕ^3$ theory up to six loops and 561 of 607 Feynman periods at seven loops. Our results support the conjectured existence of a coaction structure in quantum field theory and suggest that $ϕ^3$ and $ϕ^4$ theory share the same number content.
