论文标题
Feyngkz：使用GKZ超几何系统求解Feynman积分的Mathematica软件包
FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems
论文作者
论文摘要
在Lee-Pomeransky的代表中，Feynman积分可以被识别为Euler-Mellin积分的子集，众所周知，它们可以满足部分偏微分方程的Gel'Fand-Kapranov-Zelevinsky（GKZ）系统。在这里，我们提出了一个自动化包，以推导给定的Feynman图的关联的GKZ系统，并使用两个等效算法（即三角测量方法和Gröbner变形方法）以高几何函数的方式求解。我们以Mathematica软件包Feyngkz.wl的形式介绍我们的代码，该软件包需要SoftWares Polymake，MacAulay2和Topcom，以及包装Ambre和Olsson.wl作为依赖项。作为软件包的应用，我们找到了几个单循环和两环Feynman积分的GKZ系统的系列解决方案。这些包含在文件示例中。
In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an automated package to derive the associated GKZ system for a given Feynman diagram and solve it in terms of hypergeometric functions using two equivalent algorithms, namely the triangulation method and the Gröbner deformation method. We present our code in the form of a Mathematica package FeynGKZ.wl which requires the softwares polymake, Macaulay2 and TOPCOM, and the packages AMBRE and Olsson.wl as dependencies. As applications of the package, we find series solutions to the GKZ systems of several one-loop and two-loop Feynman integrals. These are included in the file Examples.nb that can be downloaded along with the package from https://github.com/anant-group/FeynGKZ.
