Investigations in quantum field theory

量子场论是物理学家用来描述物理世界最成功的工具之一。例如，标准模型精确地描述了所有已知粒子的行为，是一种量子场论。其他量子场论被用来描述非常有实际意义的系统，超导体和其他奇异材料，它们位于现代和未来电子设备的核心，如量子计算机。根据具体情况，量子场论可能是“弱耦合”的，也可能是“强耦合”的。弱耦合场理论是非常好理解的，并允许与详细的实验结果相匹配的精确计算。人们对强耦合场论知之甚少，也很难用于精确的计算。这一事实阻碍了我们在各种问题上的进展。这项提议的主要目的是开发新的计算工具和思想来研究强耦合量子场论。最终，我们对强耦合场论的理论理解的进步将影响我们将泰勒奇异量子系统转化为实际应用的能力，推进对宇宙基本定律的理解，并导致深刻的数学进步。

Quantum field theory is one of the most successful tools physicists use to describe the physical world. For example, the Standard Model, which describes in precise detail the behavior of all known particles, is a quantum field theory. Other quantum field theories are used to describe systems of very practical interest, superconductors and other exotic materials which lie at the core of modern and future electronic devices, such as quantum computers. Depending on the specific situation, a quantum field theory may be "weakly coupled" or "strongly coupled". Weakly coupled field theories are very well understood, and allow precise calculations which match in detail experimental results. Strongly coupled field theories are poorly understood, and very hard to use for precise calculations. This fact obstructs our progress in a variety of subjects. The main objective of this proposal is to develop new computational tools and ideas to study strongly coupled quantum field theories. Ultimately, progress in our theoretical understanding of strongly coupled field theories will impact our ability to taylor exotic quantum systems to practical applications, advance out understanding of the fundamental laws of the universe, and lead to deep mathematical advances.