Investigation of algebraic properties of gauge field theories on noncommutative spaces

非交换空间规范场论的代数性质研究

• 批准号: 5397883
• 负责人: Dr. Stefan Schraml
• 金额: --
• 依托单位: Fakultät für Physik
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2002
• 资助国家: 德国
• 起止时间: 2001-12-31 至 2003-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5397883?language=en
• 关键词: Investigation; algebraic; properties; gauge; field

The physics of space-time at very short distances is not understood. Up to now a satisfactory theory of quantum gravitation has not bee found. Infinities at short distances lead to problems for quantum field theories. A natural possibility to resolve these singularities are noncommutative spaces, since in some sense they do not possess points, or - in other words - the physical system "lives" on a lattice. The development of the last years, in particular coming also from string theory, has shown how important is an understanding of gauge theories on these spaces. Gauge theories are physical theories, which are invariant under certain symmetry transformations; the standard model and also gravitation can be formulated in this way. Objective of this research project is the investigation of such theories. Especially one should try to understand noncommutative systems with invariance under general coordinate transformations.

很短距离的时空物理学还没有被理解。到目前为止，还没有发现一个令人满意的量子引力理论。短距离的无限大给量子场论带来了问题。解决这些奇点的自然可能性是非交换空间，因为在某种意义上它们不具有点，或者换句话说，物理系统“生活”在晶格上。最近几年的发展，特别是弦理论的发展，表明了对这些空间的规范理论的理解是多么重要。规范理论是物理理论，在一定的对称变换下是不变的；标准模型和万有引力都可以用这种方式表述。本研究项目的目的就是对这些理论进行研究。人们尤其应该尝试理解在一般坐标变换下具有不变性的非交换系统。