论文标题
Feynman积分的热带蒙特卡洛正交
Tropical Monte Carlo quadrature for Feynman integrals
论文作者
论文摘要
我们介绍了一种新方法，以数字上的单纯形评估代数积分。这种新方法采用了热带几何形状的技术，并通过数量级超过了现有数值方法的能力。可以通过利用基础积分的几何结构来进一步改进该方法。为了说明这一点，我们为表现出广义定位的一类集成媒体提供了一种专门的集成算法。该类包括用于散射幅度的集成和与驯服运动学的参数Feynman积分。提供了概念验证实现，可以评估Feynman积分到循环订单17的实现。
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The method can be improved further by exploiting the geometric structure of the underlying integrand. As an illustration of this, we give a specialized integration 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.
