Mathematical Sciences: Noncommutative Geometry, Infinite Dimensional Spaces and Mathematical Physics

数学科学：非交换几何、无限维空间和数学物理

• 批准号: 9206936
• 负责人: Slawomir Klimek
• 金额: $ 5.84万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9206936&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Noncommutative; Geometry; Infinite

Klimek will continue his study of noncommutative geometry and the theory of infinite dimensional spaces. Of particular interest will be the construction of quantum Riemann surfaces and other noncommutative spaces, and application of the constructive field theory methods to analysis on infinite dimensional manifolds. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.

克利梅克将继续他对非对易几何的研究 以及无限维空间理论 特别 感兴趣的将是量子黎曼曲面的构造， 其他非对易空间，以及构造性的应用 无穷维空间分析的场论方法 流形 现代物理学，量子力学和相对论，是一个 二十世纪的产物。 它牢固地建立在 上世纪人们试图研究物质的微观结构 并掌握远距离行动的概念， 电磁和热辐射。 数学 这些发展的基础，统称为 数学物理，范围从详细分析 薛定谔算子，控制着粒子的动力学， 到统一场论，它试图统一四个已知的场论 形成一个单一的理论。