New analytic structures in gauge theories

我建议研究量子场论中的新的解析结构。我将开发新的方法来简化散射幅度的精确计算，这将使我们能够在最微观的水平上更好地理解和更准确地描述基本粒子之间的相互作用。我将依靠并推广我们最好的工具和指导原则：使用壳层上的粒子，这在过去几年已经开始产生革命性的进展。粒子物理中的实验是由量子场论定量描述的。在许多重要情况下，关键自由度之间是弱耦合的。这包括弱尺度上的强相互作用和电弱相互作用，瑞士日内瓦附近的大型强子对撞机(LHC)的实验正在积极寻找与标准模型的微小偏差。微小的耦合证明了微扰近似是合理的：它使得理论和实验的精确比较成为可能。我将致力于显著改进微扰技术。在这种情况下，量子效应传统上是用虚拟粒子的语言来理解的。最近的进展表明，当人们把注意力放在粒子来自无穷远处的观点上时，就会发生很多简化。这种粒子被称为壳上粒子，它看到了一个简单得多的世界，但似乎包含了所有必要的信息。这使得过去几年出现了令人难以置信的新计算，但这些进展大多集中在特殊情况、特殊理论或微扰理论的最低阶数上。解决这些缺点不仅对于满足对撞机实验的实际需要，而且对于我们对量子场论的基本理解都是必不可少的。*我建议直接解决两个主要瓶颈：处理提供所谓回路积分的代数表达式的组合增长，以及将Feynman积分转换为有用的解析表达式。我还建议详细研究前向散射的特殊极限。这一极限为通过前向后向关联直接接触实验提供了一个令人兴奋的新领域，此外还提供了与其他子领域进行卓有成效的相互作用的丰富机会，包括：混沌理论、通过全息术的黑洞动力学和非微扰自举。从长远来看，这项研究不仅将使大型强子对撞机和未来的对撞机在精确前沿进行新的理论计算，而且还将简化我们练习和教授量子场论的方式，并了解微观相互作用。

I propose to investigate new analytic structures in quantum field theory. I will develop new methods to simplify precision calculations of scattering amplitudes, which will allow us to better understand and describe more accurately the interactions between elementary particles at the most microscopic level. I will rely on and extend our best tool and guiding principle: the use of on-shell particles, which havs already begun to produce revolutionary advances in the past years.******Experiments in particle physics are described quantitatively by quantum field theory. In many important situations, the key degrees of freedom are weakly coupled to each other. This includes the strong and electroweak interactions at the weak scale, where experiments at the Large Hadron Collider (LHC), near Geneva in Switzerland, are actively searching for minute deviations from the Standard Model. The small coupling justifies a perturbative approximation: it enables the precise comparison of theory and experiment. I will work toward significantly improving perturbative techniques.******Quantum effects in this regime are traditionally understood in the language of virtual particles. Recent advances have shown that much simplifications occur when one focuses instead on the viewpoint of particles coming in from infinity. Such particles, called on-shell, see a much simpler world and yet appear to contain all the essential information. This has enabled incredible new calculations in the past years but much of this progress has focused on special cases, special theories or to the lowest orders in perturbation theory. Addressing these shortcomings is essential not only to meet the practical needs of collider experiments, but also to our fundamental understanding of quantum field theory.******I propose to attack directly two major bottlenecks: dealing with the combinatorial growth of the algebraic expressions which provide so-called loop integrands, and converting Feynman integrals to useful analytic expressions. I also propose to investigate in detail the special limit of forward scattering. This limit offers an exciting new area for direct contact with experiment through forward-backward correlations, in addition to rich opportunities for a fruitful interplay with other subfields, including: chaos theory, black hole dynamics through holography and the nonperturbative bootstrap. On the long term, this line of research will not only enable new theoretical calculations at the precision frontier for the LHC and future colliders, but also simplify the way we practise and teach quantum field theory and understand microscopic interactions.