论文标题
SAGEX关于散射幅度的评论，第5章：用于散射幅度及以后的分析引导程序
The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
论文作者
论文摘要
从扰动量子场理论获得对撞机实验的预测的主要挑战之一是对其产生的Feynman积分的直接评估。在本章中，我们回顾了一种替代性的引导方法，该方法相反，它通过利用其分析结构有效地构建了物理量。我们详细介绍了该方法最初开发的设置，六粒子和七粒子幅度在$ \ Mathcal {n} = 4 $ Super Yang-Mills理论的大彩色极限中。我们讨论了这些振幅所属于的功能类别，强的线索数学对象称为群集代数可用于在每个循环顺序下呈现有限和相对较小的尺寸。然后，我们描述了如何构建此功能空间，以及如何在运动限制的帮助下定位其内部的幅度，并将一般过程应用于具体示例：确定两环校正到第一个非平凡的六颗粒幅度。我们还提供了其他领域的概述，在该领域中，自举范围的范围正在扩大，包括其他散射幅度，形式因素和Feynman积分，并指出了它揭示的潜在更广泛适用性的分析性能。
One of the main challenges in obtaining predictions for collider experiments from perturbative quantum field theory, is the direct evaluation of the Feynman integrals it gives rise to. In this chapter, we review an alternative bootstrap method that instead efficiently constructs physical quantities by exploiting their analytic structure. We present in detail the setting where this method has been originally developed, six- and seven-particle amplitudes in the large-color limit of $\mathcal{N}=4$ super Yang-Mills theory. We discuss the class of functions these amplitudes belong to, and the strong clues mathematical objects known as cluster algebras provide for rendering this function space both finite and of relatively small dimension at each loop order. We then describe how to construct this function space, as well as how to locate the amplitude inside of it with the help of kinematic limits, and apply the general procedure to a concrete example: The determination of the two-loop correction to the first nontrivial six-particle amplitude. We also provide an overview of other areas where the realm of the bootstrap paradigm is expanding, including other scattering amplitudes, form factors and Feynman integrals, and point out the analytic properties of potentially wider applicability that it has revealed.
