Mathematical Sciences: Studies in Symplectic & Lorentzian Geometries

数学科学：辛研究

• 批准号: 8802672
• 负责人: Paul Ehrlich
• 金额: --
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802672&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Symplectic; &amp

Paul Ehrlich, Gerard Emch and Paul Robinson will work on problems in differential geometry and quantum theory. The questions to be addressed include geodesic incompleteness of Lorentzian manifolds, symplectic geometry of geodesics and geometric quantization. These problems are of interest in both mathematics and physics. They are fundamental to the mathematical aspects of relativity and the relationships between classical mechanics and quantum theory. Ehrlich's work focusses primarily on Lorentzian geometry and will build on recent advances made towards establishing the splitting theorem. This is related to rigidity phenomena in the singularity theory of general relativity. Emch and Robinson will investigate spinors in both the symplectic and the orthogonal contexts. These arise naturally in the attempt to geometrize the passage from classical mechanics to quantum theory where the behavior of symmetries plays an important role.

Paul Ehrlich、Gerard Emch和Paul Robinson将研究微分几何和量子理论中的问题。要解决的问题包括洛伦兹流形的测地线不完全性、测地线的辛几何和几何量子化。这些问题在数学和物理学中都很有趣。它们是相对论数学方面的基础，也是经典力学和量子理论之间关系的基础。Ehrlich的工作主要集中在洛伦兹几何学上，并将建立在建立分裂定理方面的最新进展。这与广义相对论奇点理论中的刚性现象有关。Emch和Robinson将研究辛和正交环境中的旋量。这些都是在试图几何化从经典力学到量子理论的过程中自然出现的，在量子理论中，对称性的行为起着重要的作用。