Equivariant index theory and noncommutative geometry

等变指数理论和非交换几何

• 批准号: 327638-2011
• 负责人: Emerson, Heath
• 金额: $ 1.09万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=549154
• 关键词: Equivariant; index; theory; noncommutative; geometry

The mathematical notion of a space (like the plane, or the three-dimensional space we live in, or the surface of a donut) was historically used to model physical systems, until quantum mechanics. Quantum systems are better modeled not by spaces but by certain generalizations of them called C*-algebras. The difference between the two mathematical approaches lies in a condition one may impose or not impose on `observables', namely whether or not they commute. For quantum systems, one allows noncommuting observables. The corresponding C*-algebras are noncommutative; my subject, for this reason, is sometimes called `noncommutative topology' (or `noncommutative geometry,' the latter term has been popularized by one of the main figures in the field, Alain Connes, a Field's medalist.) C*-algebras are now used extensively in many different fields of mathematics. Recently they have been used in string theory, in physics, as well.

历史上，空间的数学概念（如平面或我们居住的三维空间或甜甜圈表面）历史上用于建模物理系统，直到量子力学。量子系统更好地建模不是由空间建模，而是由它们的某些概括（称为c*orgebras）建模。两种数学方法之间的差异在于一种条件可能强加于“可观察到”，即它们是否上下班。 对于量子系统，可以允许不公开可观察到。相应的c* - 代数是非共同的；因此，我的主题有时被称为“非交通性拓扑”（或“非交易性几何形状”，后一个术语被田野中的一个主要人物普及，田野的奖章者Alain Connes。最近，它们也用于弦理论，物理学。