The Lie Algebra of Quantum Fields

量子场的李代数

• 批准号: 0401262
• 金额: $ 6.49万
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-15 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0401262&HistoricalAwards=false
• 关键词: Lie; Algebra; Quantum; Fields

The project investigates the Lie algebraic structures of perturbative quantum field theory. In particular, it will investigate the structure of the insertion-elimination Lie algebra of Feynman graphs. These algebras have a rich algebraic structure that is fundamental in understanding the structure of the quantum equations of motion and their renormalization. In particular, the relations to the Lie algebra gl(infinity) and its representation theory will be investigated. Quantum field theories underlie our understanding of the fundamental laws of nature, as well as much of materials science, in the study of phase transitions and condensed matter. These theories are typically treated as perturbation series in small observable parameters. Computation of the terms in such a series is one of the most advanced areas of computational technique. The computations have in their algebraic structures far-reaching connections to modern mathematics. This project will continue to investigate these connections to the benefit of both computational practice and conceptual foundations of the theory.

该项目研究微扰量子场论的李代数结构。 特别地，它将研究Feynman图的插入-消去李代数的结构。 这些代数具有丰富的代数结构，这对于理解量子运动方程的结构及其重整化是至关重要的。 特别是，李代数gl（无穷大）和它的表示理论的关系将被调查。 量子场论是我们理解自然界基本定律的基础，也是材料科学中相变和凝聚态研究的基础。 这些理论通常被视为小的可观测参数的扰动级数。 计算这样一个级数中的项是计算技术中最先进的领域之一。 这些计算在其代数结构中与现代数学有着深远的联系。 这个项目将继续调查这些连接的计算实践和理论的概念基础的好处。