论文标题
一种算法方法，用于寻找椭圆形积分的规范微分方程
An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
论文作者
论文摘要
近年来，微分方程已成为计算多环Feynman积分的首选方法。每当可以将它们施放为规范形式时，就可以简单地在特殊功能方面的解决方案。最近，在理解涉及椭圆聚集的Feynman积分的精确规范形式方面取得了进展。在本文中，我们利用一种算法方法，该算法证明有力地为这些情况找到规范形式。为了说明该方法，我们从文献中复制了几种已知的规范形式，并在第一次推导规范形式的示例中重现了示例。与本文一起，我们还发布了一个最初的更新，该更新是该算法的公共Mathematica实现。
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently, progress has been made in understanding the precise canonical form for Feynman integrals involving elliptic polylogarithms. In this article, we make use of an algorithmic approach that proves powerful to find canonical forms for these cases. To illustrate the method, we reproduce several known canonical forms from the literature and present examples where a canonical form is deduced for the first time. Together with this article, we also release an update for INITIAL, a publicly available Mathematica implementation of the algorithm.
