费曼积分的热带蒙特卡罗正交

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2020-08-27 DOI:10.4171/AIHPD/158
M. Borinsky
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引用次数: 34

摘要

本文提出了一种计算单纯形上代数积分的新方法。它利用热带几何学的工具改进了几何扇区分解。该方法可以通过利用底层被积函数的几何结构进一步改进。为了说明这一点,我们给出了一类表现出广义复面体形式的被积的一个特殊算法。本课程包括散射振幅的积分和参数费曼积分。提供了一个概念验证实现,可以计算循环阶为17的费曼积分。
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Tropical Monte Carlo quadrature for Feynman integrals
We introduce a new method to evaluate algebraic integrals over the simplex numerically. It improves upon geometric sector decomposition by employing tools from tropical geometry. The method can be improved further by exploiting the geometric structure of the underlying integrand. As an illustration of this, we give a specialized algorithm for a class of integrands that exhibit the form of a generalized permutahedron. This class includes integrands for scattering amplitudes and parametric Feynman integrals with tame kinematics. A proof-of-concept implementation is provided with which Feynman integrals up to loop order 17 can be evaluated.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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