标题： 费米子多面体的有限积分 显示英文标题

标题： Finite Integrals from Feynman Polytopes

摘要： 我们研究了一种几何方法，用于确定产生有限费曼积分的完整分子集。 我们的方法逐图进行，并利用与积分的西曼尼克多项式相关的牛顿多面体。 它依赖于Berkesch、Forsg{\aa }rd和Passare关于欧拉-梅林积分收敛性的定理，该定理包括费曼积分。 我们猜想，除了充分条件外，必要条件是所有参数空间单项式都位于多面体内部。 我们提出了一种基于此猜想的寻找所有有限分子的算法。 在各种例子中，我们发现使用几何方法得到的结果与Gambuti、Tancredi和两位作者开发的Landau分析方法的结果一致。 显示英文摘要

摘要： We investigate a geometric approach to determining the complete set of numerators giving rise to finite Feynman integrals. Our approach proceeds graph by graph, and makes use of the Newton polytope associated to the integral's Symanzik polynomials. It relies on a theorem by Berkesch, Forsg{\aa}rd, and Passare on the convergence of Euler--Mellin integrals, which include Feynman integrals. We conjecture that a necessary in addition to a sufficient condition is that all parameter-space monomials lie in the interior of the polytope. We present an algorithm for finding all finite numerators based on this conjecture. In a variety of examples, we find agreement between the results obtained using the geometric approach, and a Landau-analysis approach developed by Gambuti, Tancredi, and two of the authors.