Application of methods of arithmetic geometry and homological algebra to quantum field theory and string theory

算术几何和同调代数方法在量子场论和弦论中的应用

• 批准号: 0805989
• 负责人: Albert Schwarz
• 金额: $ 19.63万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805989&HistoricalAwards=false
• 关键词: Application; methods; arithmetic; geometry; homological

AbstractAward: DMS-0805989Principal Investigator: Albert SchwarzThe first of these projects concerns applications of p-adicmethods to topological strings. The goal of these projects is toexpress physical quantities in terms of arithmetic geometry overp-adic numbers and to use these expressions to prove integralitytheorems. Another set of investigations deals withsupersymmetric deformations of quantum field theories. This isjoint work with M. Movshev and applies the theory of L-infinityand A-infinity algebras. Another project is devoted to theanalysis of the relation between string theory and quantum fieldtheory. The principal investigator has argued that quantum fieldtheory can be formulated such that time and space do not appearas primary notions, and is planning to show that string theorycan be regarded as a quantum field theory in this sense.These research projects are based on the application of methodsof modern mathematics to physics, particularly making use ofarithmetic geometry and homological algebra to improve ourunderstanding of quantum field theory and string theory.Sophisticated mathematics originally developed for other purposessuch as the study of Diophantine equations in number theory seemsto bear directly on challenging issues in theoretical physics.

摘要奖项：DMS-0805989 首席研究员：Albert Schwarz 第一个项目涉及 p-adic 方法在拓扑字符串中的应用。这些项目的目标是用算术几何超过基本数来表达物理量，并使用这些表达式来证明完整性定理。 另一组研究涉及量子场论的超对称变形。 这是与 M. Movshev 的合作成果，应用了 L-无穷大和 A-无穷大代数理论。 另一个项目致力于分析弦理论和量子场论之间的关系。首席研究员认为，量子场论可以被表述为时间和空间不再是主要概念，并计划证明弦论在这个意义上可以被视为量子场论。这些研究项目基于现代数学方法在物理学中的应用，特别是利用算术几何和同调代数来提高我们对量子场论和弦论的理解。 最初是为其他目的而开发的，例如数论中丢番图方程的研究，似乎直接涉及理论物理学中的挑战性问题。