Space-Time from the Spectral Point of View: Towards Quantum Gravity

从光谱角度看时空：走向量子引力

• 批准号: 1202671
• 负责人: Ali Chamseddine
• 金额: $ 15万
• 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: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1202671&HistoricalAwards=false
• 关键词: Space; Time; Spectral; Point; View

The most challenging problem in theoretical physics is the unification of the laws of quantum physics with Einstein's 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. In the past years it has been established that space-time is approximated by a well defined product of a continuous four-dimensional manifold by a finite dimensional space. The main focus of this program is to construct a genuinely noncommutative finite dimensional space valid at sub-planckian scales and whose limit at lower energies is the noncommutative space of the standard model. The geometry will be reduced to those of almost commuting matrices, and it will be possible to get a handle on quantizing the geometry. It will also study new asymptotic limits of the spectral action as well as cosmological implications. Other parts of this project will study various aspects of gravity such as stability of BPS monopoles, and formulation of consistent massive theories of gravity, implications of the presence of right-handed neutrinos on the geometry of spacetime, the behavior of spectral actions in the presence of singularities and non-perturbative evolution of the dynamical fields at scales of the order of the Planck length. Broader impact of Project: Due to its interdisciplinary nature, this work which involves research on the frontiers of noncommutative geometry, will be of benefit to both physicists and mathematicians. The new ideas and methods in this proposal will contribute to the knowledge of the high energy theory and phenomenology, quantum gravity and mathematics communities, and to a lesser extent to the astro-physics community. The American University of Beirut (AUB) plays a very important role in promoting the American educational system in the Middle East. Historically, the emphasis was on liberal education. The new aim is to provide in addition a vibrant environment for the promotion of research. The launching of the Ph.D. program in theoretical physics in October 2009 is a step in that direction and is attracting students of high caliber.

理论物理学中最具挑战性的问题是量子物理定律与爱因斯坦的广义相对论的统一。在这个方向上，人们最有力地追求的思想是超弦理论和非对易几何。这两种方法密切相关。非对易几何为研究黎曼几何的标准方法所不能处理的空间提供了一个新的框架。它为规范理论和希格斯场的作用的研究提供了一个新的视角，并且是描述普朗克能量下几何的一个有希望的候选者。在过去的几年里，人们已经建立了时空近似于一个连续的四维流形的有限维空间的良好定义的产品。这个计划的主要重点是构建一个真正的非对易有限维空间有效的亚普朗克尺度和其限制在较低的能量是非对易空间的标准模型。几何将被减少到几乎可交换矩阵的几何，并且将有可能处理几何的量化。它还将研究光谱作用量的新的渐近极限以及宇宙学意义。这个项目的其他部分将研究引力的各个方面，如BPS单极子的稳定性，一致的大质量引力理论的制定，右手中微子的存在对时空几何的影响，在奇点存在下的光谱作用的行为和普朗克长度量级的动力场的非微扰演化。项目的更广泛影响：由于其跨学科的性质，这项工作涉及非对易几何的前沿研究，将有利于物理学家和数学家。该建议中的新思想和方法将有助于高能理论和现象学，量子引力和数学社区的知识，并在较小程度上有助于天体物理学社区。贝鲁特美国大学（AUB）在中东地区推广美国教育体系方面发挥着非常重要的作用。从历史上看，重点是自由教育。新的目标是为促进研究提供一个充满活力的环境。博士学位的启动。2009年10月的理论物理课程是朝着这个方向迈出的一步，吸引了高素质的学生。