Noncommutative geometry in representation theory and quantum physics

表示论和量子物理中的非交换几何

• 批准号: DP0986551
• 负责人: Prof Ruibin Zhang
• 金额: $ 32.22万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2009
• 资助国家: 澳大利亚
• 起止时间: 2009-02-26 至 2014-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0986551
• 关键词: Noncommutative; geometry; representation; theory; quantum

One of the most important problems in natural science is to understand the structure of spacetime at the Planck scale. Mathematical investigations in recent years have predicted that at this scale, spacetime becomes noncommutative. Taking this noncommutativity into account, the project brings together geometry, algebra and quantum mechanics to develop new mathematical theories required for addressing the problem. It promises to make fundamental contributions to both mathematics and theoretical physics.

自然科学中最重要的问题之一是在普朗克尺度上理解时空的结构。最近几年的数学研究预测，在这个尺度上，时空变得非对易。考虑到这种不可交换性，该项目将几何、代数和量子力学结合在一起，开发出解决这个问题所需的新的数学理论。它有望为数学和理论物理做出根本性的贡献。