Geometry and representations of classical and quantum Lie supergroups

经典和量子李超群的几何和表示

• 批准号: DP0451790
• 负责人: Prof Ruibin Zhang
• 金额: $ 12.53万
• 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: 2004
• 资助国家: 澳大利亚
• 起止时间: 2004-04-01 至 2007-11-28
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0451790
• 关键词: Geometry; representations; classical; quantum; Lie

The physical notion of supersymmetry is a unifying principle which ensures that bosonic and fermionic particles in quantum physics obey the same fundamental laws. It has permeated the forefront of mathematical research since 1980s, leading to the creation of some of the deepest theories in diverse areas. The mathematical foundation of supersymmetry lies in the theory of Lie supergroups. This project addresses major outstanding problems in the geometry and representations of Lie supergroups and their quantum analogues. Results will be important to the quest for a consistent quantum theory of all the four interactions in nature.

超对称性的物理概念是一个统一的原则，它确保量子物理学中的玻色子和费米子粒子遵守相同的基本定律。自20世纪80年代以来，它已经渗透到数学研究的最前沿，导致在不同领域创建了一些最深刻的理论。超对称性的数学基础在于李群理论。这个项目解决了李群及其量子类似物的几何和表示中的主要突出问题。结果对于寻求自然界所有四种相互作用的一致量子理论非常重要。