论文标题
Feynman参数通过微分方程集成
Feynman parameter integration through differential equations
论文作者
论文摘要
我们提出了一种用于计算通用多环Feynman积分的新方法。该方法依赖于Feynman的诀窍在结合两个繁殖器中的迭代应用。 Feynman的技巧的每个应用都引入了简化的Feynman积分拓扑，该拓扑取决于应该集成的Feynman参数。对于每个积分家族，我们建立了一个微分方程的系统，我们根据Feynman参数中的广义系列扩展集合来解决。这些广义串联扩展可以按学期有效地集成，并按细分细分市场进行分段。这种方法导致一种完全算法的方法来计算来自微分方程的Feynman积分，该方程不需要手动确定边界条件。此外，该方法中出现的最复杂的拓扑通常比原始积分较少。我们用五点两环积分家族说明了我们方法的强度。
We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a simplified Feynman integral topology which depends on a Feynman parameter that should be integrated over. For each integral family, we set up a system of differential equations which we solve in terms of a piecewise collection of generalized series expansions in the Feynman parameter. These generalized series expansions can be efficiently integrated term by term, and segment by segment. This approach leads to a fully algorithmic method for computing Feynman integrals from differential equations, which does not require the manual determination of boundary conditions. Furthermore, the most complicated topology that appears in the method often has less master integrals than the original one. We illustrate the strength of our method with a five-point two-loop integral family.
