论文标题
Sagex关于散射幅度的评论，第4章：多环Feynman积分
The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
论文作者
论文摘要
多环Feynman积分对特殊功能和常数的分析整合和简化在基本颗粒的标准模型中执行高阶扰动计算起着重要作用。在这篇调查文章中，介绍了当前使用的最新和相关的计算机代数和特殊功能算法，或者可能在将来执行此类挑战性的精确计算中起重要作用。它们是在标准模型和有效场理论的量子场理论中的分析零，单一和双尺度计算的背景下进行讨论的。这些计算在目前和将来的山脉分析目前和将来的山脉分析中起着核心作用，以获取基本物理学的最终信息。
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this survey article the most recent and relevant computer algebra and special function algorithms are presented that are currently used or that may play an important role to perform such challenging precision calculations in the future. They are discussed in the context of analytic zero, single and double scale calculations in the Quantum Field Theories of the Standard Model and effective field theories, also with classical applications. These calculations play a central role in the analysis of precision measurements at present and future colliders to obtain ultimate information for fundamental physics.
