Combinatorial approaches to quantum field theory

量子场论的组合方法

• 批准号: RGPIN-2014-06146
• 负责人: Yeats, Karen
• 金额: $ 1.68万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612056
• 关键词: Combinatorial; approaches; quantum; field; theory

Quantum field theory describes our universe over an enormous range of orders of magnitude and at very high precision. It is also full of beautiful patterns and structures. The goal of this research program is increase understanding of quantum field theory by furthering our combinatorial understanding of the underlying patterns in Feynman graphs, Feynman integrals, and their combinations into physically meaningful quantities. In particular, this proposal seeks first to give a graph theoretical understanding of the connection between graphs and transcendental values through their Feynman integrals, and second to understand the recursive decomposition of Feynman graphs into subgraphs along with the analytic version of this decomposition, the Dyson-Schwinger equations. The outcome of this work will be a better understanding of the fundamental theories which make up our universe as well as rich and beautiful mathematical objects and results. This proposal will incorporate the training of students at all levels in both pure and applied skills. The work is collaborative, enhancing my own strengths with those of other researchers, to yield innovative results. This work is of value both as pure mathematics and as mathematical physics, and gives Canada a place in this cutting edge approach to quantum field theory.

量子场论在数量级的巨大范围内以非常高的精度描述了我们的宇宙。它也充满了美丽的图案和结构。这项研究计划的目标是通过进一步加深我们对费曼图、费曼积分及其组合成物理上有意义的量的潜在模式的组合理解，来增加对量子场论的理解。