论文标题
法格曼尼亚人的Feynman积分
Feynman Integrals of Grassmannians
论文作者
论文摘要
我们通过在投射空间中的综合体的均质化将Feynman积分嵌入了司芒氏菌的亚地区，然后获得这些标量积分满足的GKZ系统。 Feynman积分可以写为基本解决方案系统在GKZ-System的常规奇异性邻里的超几何函数的线性组合，其线性组合系数由正常点或一些规则的奇异性确定。以一些Feynman图为例，我们详细阐述了如何在常规奇异点附近获得Feynman积分的基本解决方案系统。此外，我们还介绍了2环的自能量图的Feynman积分的参数表示，这些图很方便地嵌入了司司曼尼亚的亚地区。
We embed Feynman integrals in the subvarieties of Grassmannians through homogenization of the integrands in projective space, then obtain GKZ-systems satisfied by those scalar integrals. The Feynman integral can be written as linear combinations of the hypergeometric functions of a fundamental solution system in neighborhoods of regular singularities of the GKZ-system, whose linear combination coefficients are determined by the integral on an ordinary point or some regular singularities. Taking some Feynman diagrams as examples, we elucidate in detail how to obtain the fundamental solution systems of Feynman integrals in neighborhoods of regular singularities. Furthermore we also present the parametric representations of Feynman integrals of the 2-loop self-energy diagrams which are convenient to embed in the subvarieties of Grassmannians.
