论文标题
Sagex关于散射幅度的评论，第7章：散射幅度的正数几何形状
The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
论文作者
论文摘要
散射幅度既是一个很棒的操场，可以在量子场理论中发现新思想，并且同时具有巨大的现象学重要性，以对例如粒子碰撞器可观察到的精确预测，而最近也对引力波信号进行了预测。在本综述一章中，我们概述了一些令人兴奋的在数学，几何数量（例如多面体，Associahedra，Grassmanians和agplituhedron）方面重新重新设计QFT的令人兴奋的进展。在这种新颖的方法中，标准的局部和单位性概念是构成的概念，而不是结构中的基本要素，这可能使我们可以解决QFT中许多开放问题的概念，这些问题已经避免了数十年的答案。我们首先给出了积极几何形状的基本摘要，然后再讨论AssociaHedron（最简单的物理相关几何示例之一）及其与Bi-Adychoint $ ϕ^3 $理论中的树级散射幅度的关系。我们的第二个示例是用于在平面最大超对称阳米尔斯理论中散射幅度的扩增的构造。
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more recently also for gravitational wave signals. In this review chapter, we give an overview of some of the exciting recent progress on reformulating QFT in terms of mathematical, geometric quantities, such as polytopes, associahedra, Grassmanians, and the amplituhedron. In this novel approach, standard notions of locality and unitarity are derived concepts rather than fundamental ingredients in the construction which might give us a handle on a number of open questions in QFT that have evaded an answer for decades. We first give a basic summary of positive geometry, before discussing the associahedron -- one of the simplest physically relevant geometric examples -- and its relation to tree-level scattering amplitudes in bi-adjoint $ϕ^3$ theory. Our second example is the amplituhedron construction for scattering amplitudes in planar maximally supersymmetric Yang-Mills theory.
