论文标题
Sagex关于散射幅度的评论，第3章：Feynman积分中的数学结构
The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
论文作者
论文摘要
尺寸调节的Feynman积分是量子场理论中所有扰动计算的基石。众所周知，它们表现出丰富的数学结构，这导致了其计算的强大新技术的发展。我们回顾了我们对多尺度正规化中多核feynman积分分析结构的理解的最新进展。特别是，我们概述了使用微分方程计算Feynman积分的现代方法，并讨论了解决方案中出现的功能的某些属性。然后，我们回顾了维度正则化如何根据扭曲的共同学组理论具有自然的数学解释，以及在这种情况下自然出现了关于Feynman积分的知名观念。这是有关散射幅度的一系列评论文章的第3章，其中第0章[ARXIV：2203.13011]介绍了概述，第4章[Arxiv：2203.13015]包含密切相关的主题。
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for their computation. We review some of the most recent advances in our understanding of the analytic structure of multiloop Feynman integrals in dimensional regularisation. In particular, we give an overview of modern approaches to computing Feynman integrals using differential equations, and we discuss some of the properties of the functions that appear in the solutions. We then review how dimensional regularisation has a natural mathematical interpretation in terms of the theory of twisted cohomology groups, and how many of the well-known ideas about Feynman integrals arise naturally in this context. This is Chapter 3 of a series of review articles on scattering amplitudes, of which Chapter 0 [arXiv:2203.13011] presents an overview and Chapter 4 [arXiv:2203.13015] contains closely related topics.
