New analytic structures in gauge theories

我打算研究量子场论中新的解析结构。 我将开发新的方法来简化散射振幅的精确计算，这将使我们能够更好地理解和更准确地描述最微观水平上的基本粒子之间的相互作用。 我将依赖并扩展我们最好的工具和指导原则：使用壳层粒子，在过去几年中，它已经开始产生革命性的进步。量子场论定量地描述了粒子物理学中的实验。 在许多重要的情况下，关键自由度彼此弱耦合。 这包括弱尺度下的强相互作用和电弱相互作用，在瑞士日内瓦附近的大型强子对撞机（LHC）上的实验正在积极寻找与标准模型的微小偏差。 小的耦合证明了微扰近似：它使理论和实验的精确比较成为可能。 我将致力于显著改善微扰技术。传统上，这个领域的量子效应是用虚粒子的语言来理解的。 最近的进展表明，当人们把注意力集中在粒子来自无穷远的观点上时，就会出现许多简化。 这种粒子被称为壳层上粒子，它看到的是一个简单得多的世界，但似乎包含了所有的基本信息。 这使得令人难以置信的新的计算在过去几年中，但大部分这方面的进展集中在特殊情况下，特殊的理论或最低阶微扰理论。 解决这些缺点不仅对满足对撞机实验的实际需要至关重要，而且对我们对量子场论的基本理解也至关重要。我建议直接攻击两个主要的瓶颈：处理的组合增长的代数表达式，提供所谓的循环被积函数，并转换费曼积分有用的解析表达式。 我还建议详细研究前向散射的特殊极限。 这个极限提供了一个令人兴奋的新领域，通过向前向后的相关性与实验直接接触，除了丰富的机会，富有成效的相互作用与其他子领域，包括：混沌理论，黑洞动力学通过全息和非微扰自举。 从长远来看，这一研究方向不仅将为LHC和未来的对撞机提供精确前沿的新理论计算，而且还将简化我们实践和教授量子场论以及理解微观相互作用的方式。

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.