Quantum differential geometric methods in theoretical physics

理论物理中的量子微分几何方法

• 批准号: 2609634
• 金额: --
• 依托单位: Queen Mary University of London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2609634
• 关键词: Quantum; differential; geometric; methods; theoretical

Quantum differential geometry was developed in recent years as an extension to geometry to allow the "coordinate algebra" of a space to be noncommutative and/or for differential forms to not commute with coordinates.Our current project consists of applying these mathematical concepts to theoretical and mathematical physics in order to have a description of physics when the underlying spacetime is noncommutative. Specifically, we are adapting the main constructions of classical field theory, such as the jet bundle and the variational bicomplex, to noncommutative spacetimes. This would then allow for the first time a systematic formulation of the Euler-Lagrange equations and Noether theorems for noncommutative spacetimes.

量子微分几何是近年来发展起来的几何学的一个扩展，它允许空间的“坐标代数”是非对易的，并且/或者允许微分形式不与坐标对易。我们目前的项目包括将这些数学概念应用到理论物理和数学物理中，以便在基础时空是非对易的情况下描述物理。具体地说，我们正在调整经典场论的主要结构，如喷束和变分双复，非对易时空。这将允许第一次系统地表述非对易时空的欧拉-拉格朗日方程和诺特定理。