Mathematical Sciences: Mathematical Physics and Noncommutative Differential Geometry

数学科学：数学物理和非交换微分几何

• 批准号: 9404481
• 负责人: Ezra Getzler
• 金额: $ 8.07万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404481&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Physics; Noncommutative; Differential

9404481 Getzler The research entails a number of topics in the relatively new area of topological field theory with applies methods of homological algebra and algebraic topology to concepts in modern quantum field theory and superstrings. Particular importance will be paid to the development of the cyclic Chern character and the index of classes of pseudodifferential operators in the setting of non-commutative differential geometry. The topics studied here are considered as fundamental in modern mathematical physics. ***

9404481盖茨勒这项研究涉及拓扑场论相对较新的领域中的许多主题，将同调代数和代数拓扑的方法应用于现代量子场论和超弦中的概念。在非对易微分几何的背景下，将特别重视循环陈特征标和拟微分算子类的指数的发展。这里研究的课题被认为是现代数学物理的基础。***