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将在差异几何学和量子理论方面致力于问题。要解决的问题包括Lorentzian歧管的大地测量不完整，地球学的符号几何以及几何量化。这些问题在数学和物理学中都引起了人们的关注。它们是相对论的数学方面以及经典力学与量子理论之间的关系。 埃里希（Ehrlich）的作品主要集中在洛伦兹（Lorentzian）的几何形状上，并将基于建立分裂定理的最新进展。这与一般相对性的奇异性理论中的僵化现象有关。 Emch和Robinson将在符号和正交环境中研究旋转器。这些自然出现的是将从经典力学到量子理论的段落几何来源，在这种理论中，对称性的行为起着重要作用。