High-Energy Physics

粒子物理学在最短的距离上提供了对物质的非常精确的描述：标准模型，一种特殊的量子场论。随着实验积极寻找标准模型之外的物理学线索，特别是在大型强子对撞机上，与理论的详细比较变得越来越重要。量子场之间的相互作用可以是弱的，也可以是强的。这个提议将发展新的分析技术来计算这两种情况，并限制引力相互作用。这个提议建立在一个强有力的认识基础上：通常存在一个唯一的量子场论，它与给定的对称性和普适性原理相容。量子场论诞生于相对论和量子力学的结合，近年来的发展表明，由于这种独特性，从最基本的原理出发是一种非常有效的计算策略。散射振幅的精确计算是粒子物理学的基础：它们描述了碰撞所有可能结果的相对概率。近年来，所谓的壳层方法在弱耦合近似下，通过利用基本原理将复杂过程分解为简单过程，大大提高了精度。这个建议将解决下一代振幅计算的突出挑战，特别是如何胶回子过程，带来新的数学工具，从代数geometrics.Beyond弱耦合，bootstrap方法已成功地应用于共形（无标度）理论。这一建议将扩大其使用散射振幅在更一般的模型，包括理论的强力。申请人的小组将开发精确的求和规则，以限制中等能量弱耦合近似中的误差。同样的技术也将应用于引力子的散射。在目前缺乏一个独特的量子引力预测理论的情况下，重要的是要限制可能性：因果理论与爱因斯坦的广义相对论有什么不同？该研究将对标准模型过程的精度计算产生直接影响。可以直接从一般原理中提取定量预测的概念意义深远。它将对许多子领域的从业者理解、使用和教授微观相互作用的方式产生深远而持久的影响。

Particle physics provides an extraordinarily precise description of matter at the shortest of distances: the Standard Model, a particular quantum field theory. As experiments actively search for hints of physics beyond the Standard Model, notably at the Large Hadron Collider, detailed comparison with theory becomes increasingly crucial. Quantum fields can interact weakly or strongly, and this proposal will develop new analytic techniques to calculate in these two regimes, and to constrain gravitational interactions.This proposal builds on a powerful realization: there is often a unique quantum field theory compatible with given symmetries and universal principles. Quantum field theory was born of the union of relativity and quantum mechanics, and developments from recent years have shown that, thanks to this uniqueness, starting from the most basic principles is a very effective strategy for calculations.Precision calculations of scattering amplitudes are fundamental to particle physics: they describe the relative probabilities of all the possible outcomes of a collision. So-called on-shell approaches have dramatically improved precision in recent years, in a weak coupling approximation, by exploiting basic principles to break complicated processes into simpler ones. This proposal will address outstanding challenges for the next generation of amplitude calculations, notably how to glue back subprocesses, by bringing new mathematical tools from algebraic geometry.Beyond weak coupling, bootstrap methods have been successfully applied to conformal (scale-less) theories. This proposal will extend their use to scattering amplitudes in more general models, including the theory of the strong force. The applicant's group will develop exact sum rules to bound errors in the weak coupling approximation at intermediate energies. The same techniques will be applied to scattering of gravitons. In the current absence of a unique predictive theory of quantum gravity, it is important to limit the possibilities: How different from Einstein's general relativity could a causal theory be?This research will have a direct impact on the field of precision calculations of Standard Model processes. The notion that quantitative predictions can be extracted directly from general principles is far-reaching. It will have a profound and long-lasting influence on the way microscopic interactions are understood, used, and taught by practitioners in many subfields.