Algebraic structures in perturbative quantum field theory

微扰量子场论中的代数结构

• 批准号: 1007168
• 负责人: Kevin Costello
• 金额: $ 24.97万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007168&HistoricalAwards=false
• 关键词: Algebraic; structures; perturbative; quantum; field

AbstractAward: DMS-1007168Principal Investigator: Kevin J. CostelloThe proposed research is concerned with a new approach to perturbative quantum field theory, based on the concept of a actorization algebra. Factorization algebras are rich algebraic objects which simultaneously generalize the notion of E-n algebra and that of chiral algebra. The aim of this proposal is to show that the techniques of perturbative renormalization allow one to construct factorization algebras starting from a Lagrangian defining a physical system. Several applications of this approach to quantum field theory are also being proposed, including one related to elliptic cohomology and the Witten genus.Quantum field theory is a fundamental tool in theoretical hysics, and underpins physicists current understanding of the behaviour of elementary particles. Quantum field theory has additionally had a great influence on the development of mathematics. The aim of this research proposal is to provide mathematical foundations for quantum field theory, and to apply these foundations to problems in geometry related to physics.

AbstractAward：DMS-1007168首席研究员：Kevin J. Costello拟议的研究涉及一种新的微扰量子场论方法，基于作用代数的概念。 因子分解代数是一个丰富的代数对象，它同时推广了E-n代数和手征代数的概念。 这个建议的目的是表明，微扰重整化的技术允许一个从定义一个物理系统的拉格朗日开始构造因子分解代数。 这种方法在量子场论中的一些应用也被提出，包括椭圆上同调和维滕亏格。量子场论是理论物理学中的一个基本工具，支撑着物理学家目前对基本粒子行为的理解。 量子场论也对数学的发展产生了巨大的影响。 这项研究计划的目的是为量子场论提供数学基础，并将这些基础应用于与物理学相关的几何问题。