论文标题
Feynman积分的Macaulay矩阵：线性关系和交叉数字
Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
论文作者
论文摘要
我们详细介绍了Gel'Fand-Kapranov-Zelevinsky系统，扭曲的同胞组的DE RHAM理论和Feynman积分方程。我们提出了一种新型，更有效的算法来计算曲线矩阵，该矩阵用于得出微分方程的Pfaffian系统。然后，使用PFAFFIAN矩阵来获得$ {\ cal a} $ - 超几何（Euler）积分和Feynman积分的线性关系，通过复发关系和通过交叉数字进行预测。
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for ${\cal A}$-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.
