New analytic structures in gauge theories

规范理论中的新分析结构

• 批准号: SAPIN-2017-00034
• 负责人: CaronHuot, Simon
• 金额: $ 3.28万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646891
• 关键词: New; analytic; structures; gauge; theories

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.

我提议在量子场论中研究新的解析结构。我将开发新的方法来简化散射振幅的精确计算，这将使我们能够在最微观的层面上更好地理解和更准确地描述基本粒子之间的相互作用。我将依靠并扩展我们最好的工具和指导原则：使用壳上粒子，这在过去几年中已经开始产生革命性的进展。******粒子物理学中的实验是用量子场论定量描述的。在许多重要的情况下，关键自由度彼此之间是弱耦合的。这包括弱尺度下的强和电弱相互作用，在瑞士日内瓦附近的大型强子对撞机（LHC）的实验中，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的合理性：它使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。******这种状态下的量子效应传统上是用虚粒子的语言来理解的。最近的进展表明，当人们转而关注从无穷远处来的粒子的观点时，会发生许多简化。这种粒子被称为上壳粒子，它们看到的是一个简单得多的世界，却似乎包含了所有的基本信息。在过去的几年里，这使得令人难以置信的新计算成为可能，但这些进展大多集中在特殊情况、特殊理论或摄动理论的最低阶上。解决这些缺陷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瓶颈：处理提供所谓循环积分的代数表达式的组合增长，以及将费曼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。这一极限提供了一个令人兴奋的新领域，通过向前-向后关联直接接触实验，除了丰富的机会与其他子领域，包括：混沌理论，黑洞动力学通过全息和非摄动自举。从长远来看，这条研究路线不仅将为大型强子对撞机和未来的对撞机提供高精度的新理论计算，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。