Feynman integrals appropriately generalized are -hypergeometric functions. Among the properties of -hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions these symmetries lead to linear transformations. Combining tools of -hypergeometric systems and the computation of symmetries of polytopes, we consider the associated symmetries of Feynman integrals in the Lee-Pomeransky representation. We compute the symmetries of -gon integrals up to , massive banana integrals up to 5-loop, and on-shell ladders up to 3-loop. We apply these symmetries to study finite on-shell ladder integrals up to 3-loop.

中文翻译：

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费曼积分的多面体对称性


适当推广的费曼积分是超几何函数。超几何函数的属性之一是与牛顿多面体相关的对称性。在普通的超几何函数中，这些对称性导致线性变换。结合超几何系统的工具和多面体对称性的计算，我们考虑 Lee-Pomeransky 表示中费曼积分的相关对称性。我们计算高达 的 -gon 积分、高达 5 环的大香蕉积分以及高达 3 环的壳上梯子的对称性。我们应用这些对称性来研究最多 3 环的有限壳上梯积分。