Unification, Quantum Gravity and Noncommutative Geometry

统一、量子引力和非交换几何

• 批准号: 0653300
• 负责人: Ali Chamseddine
• 金额: $ 0.5万
• 依托单位: American University of Beirut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-10-01 至 2009-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0653300&HistoricalAwards=false
• 关键词: Unification; Quantum; Gravity; Noncommutative; Geometry

A challenging problem in theoretical physics is the unification of the laws of quantum physics with Einstein general theory of relativity. The ideas in this direction that have been pursued most forcefully are superstring theory and noncommutative geometry. These two approaches are intimately related. Noncommutative geometry has provided a new framework to study spaces which could not be handled by the standard methods of Riemannian geometry. It offered a new perspective in the study of gauge theories and the role of the Higgs field and is a promising candidate to describe geometries at Planckian energies. The main focus of this proposal is to study the nature of space-time at sub- Planckian scales and to find its geometric properties and thus determine the dynamics. The broader impact of this research is that the research involves work on the frontiers of noncommutative geometry and will be of benefit to both physicists and mathematicians.

理论物理学中的一个具有挑战性的问题是量子物理定律与爱因斯坦广义相对论的统一。在这个方向上最有力地追求的思想是超弦理论和非交换几何。这两种方法密切相关。非交换几何为研究黎曼几何标准方法无法处理的空间提供了一个新的框架。它为规范场理论和希格斯场的作用的研究提供了新的视角，并且是描述普朗克能量几何的有希望的候选者。该提案的主要重点是研究亚普朗克尺度的时空本质，并找到其几何特性，从而确定动力学。这项研究更广泛的影响是，该研究涉及非交换几何的前沿工作，将对物理学家和数学家都有好处。