From Symmetries to Geometry and Beyond: a Modern Approach to Scattering Amplitudes

该项目的目标是为量子场论（QFT）的现代方法提供重要的步骤，特别是通过对散射振幅的新理解。QFT是物理学中最成功的数学框架之一。它的传统出发点是拉格朗日：从它导出的费曼规则允许计算微扰物理量。其中，一个突出的作用是由散射振幅，描述粒子之间的相互作用。标准的费曼计算已经取得了巨大的进展，在理论上预测的振幅直接相关的实验在高能对撞机。然而，有强有力的证据表明，更根本的、潜在的原则还有待发现。一个重要的迹象失踪的原则是显着的简单的最终结果的振幅，尽管复杂的中间计算在传统的费曼展开。 这在精确可解的量子场论中非常明显，例如平面最大超对称杨-米尔斯理论，其中振幅和理论本身的新见解是由涌现的无限维对称性提供的，而不是从标准的费曼方法中表现出来。此外，还提出了新的振幅几何表达式，这些表达式尽可能地远离任何传统的表示。 QFT的标准基础，如统一性和局部性，不是显而易见的，而是自然出现的。对对称性和基本几何性质的研究，使得从拉格朗日的观点无法得到可能的发展。该项目探索这些迷人的问题，旨在分析最大超对称杨-米尔斯理论的显着特性，重点关注其对称性，新的计算技术和基于振幅几何化的基本见解。这为引力理论和量子色动力学的新观点提供了基础。

The goal of this project is to provide significant steps towards a modern approach to Quantum Field Theories (QFT), especially through a novel understanding of scattering amplitudes.QFT is among the most successful mathematical frameworks in physics. Its traditional starting point is a Lagrangian: the Feynman rules derived from it allow to compute perturbatively physical quantities. Among these, a prominent role is played by scattering amplitudes, describing the interactions between particles. Standard Feynman computations have made possible tremendous progress in giving theoretical predictions for amplitudes of direct relevance for experiments at high-energy colliders. There is, however, strong evidence that more fundamental, underlying principles have yet to be discovered. A significant indication of a missing principle is the remarkable simplicity of final results for amplitudes, despite the complexity of intermediate computations in the traditional Feynman expansion. This is very evident in exactly solvable QFTs, such as planar maximally supersymmetric Yang-Mills theory, where novel insights for amplitudes and for the theories themselves are provided by, for instance, emergent infinite dimensional symmetries and are not manifest from a standard Feynman approach. Furthermore, new geometric formulations for amplitudes have been proposed, which are far away from any traditional presentation as possible. The standard foundations of QFTs, such as unitarity and locality, are not manifest but rather emerge naturally. Investigations of symmetries and fundamental, geometric properties have made possible developments not accessible from a Lagrangian point of view. This project explores these fascinating questions and is aimed at analysing the remarkable properties of maximally supersymmetric Yang-Mills theory, focusing on its symmetries, new computational technologies and fundamental insights based on the geometrization of amplitudes. This offers the basics for a novel point of view on gravity theories and Quantum Chromodynamics.