Tropical sampling from Feynman measures

We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an implementation, momtrop, and apply it to a series of relevant integrals from the loop-tree duality framework. Compared to naive sampling methods, we observe convergence speedups by factors of more than 10^6.

本文提出一种算法，可对按给定费曼被积函数（Feynman integrand）分布的一组圈动量进行采样。该算法采用热带采样法（tropical sampling method），可高效求解相空间型积分。本文提供了名为momtrop的实现代码，并将其应用于圈树对偶框架（loop-tree duality framework）下的一系列相关积分。相较于朴素采样法，本文观测到其收敛加速倍率超过10^6。