论文标题
从单一均匀重量积分中得出Feynman积分的规范微分方程
Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
论文作者
论文摘要
微分方程是评估Feynman积分的强大工具。如果找到向规范形式的转换，他们的解决方案是直接的。在本文中，我们提出了一种用于查找这种转换的算法。这项新型技术基于Hoschele等人引起的方法。并且仅依靠统一的先验重量的单个积分的知识。作为推论，该算法也可用于测试给定积分的均匀超屈态。我们讨论了几个尖端示例的应用，包括非平面四环HQET和非平面二环积分。本文提供了我们算法的数学实现。
Differential equations are a powerful tool for evaluating Feynman integrals. Their solution is straightforward if a transformation to a canonical form is found. In this paper, we present an algorithm for finding such a transformation. This novel technique is based on a method due to Hoschele et al. and relies only on the knowledge of a single integral of uniform transcendental weight. As a corollary, the algorithm can also be used to test the uniform transcendentality of a given integral. We discuss the application to several cutting-edge examples, including non-planar four-loop HQET and non-planar two-loop five-point integrals. A Mathematica implementation of our algorithm is made available together with this paper.
