Mathematical Sciences: Operator Algebras, Quantization, and Supersymmetry

小行星9424344 建议在新的方向上继续和扩大正在进行的 研究量子化空间和超空间的程序， 算子代数与非交换微分技巧 几何该计划的目标是：（1）了解系统的量化数学（包括 无限和无限多个自由度）， 相空间几何;（2）研究微观世界物理学的非对易几何原理，特别是可能的含义 （3）探索新的数学现象，将分析与其他 数学领域。 非对易几何是八十年代创立的一个新的数学方向。它的主要目的是研究物体，称为 非交换空间或流形，不是普通的几何空间 但仍然有几何的味道。这种结构的例子自然出现，例如在亚原子的物理理论中， 现象。非对易几何方法成为了一个强有力的工具 在研究现代分析和理解的各种问题， 微观世界物理学的基础。提出要 研究非交换流形的例子，重点放在量子物理学的应用上。此外，建议将 量子理论中的一些观点 现代分析。 ***

9424344 Lesniewski It is proposed to continue and expand in new directions an ongoing program of studying quantized spaces and superspaces by means of the techniques of operator algebras and non-commutative differential geometry. The goals of the program are: (1) To understand the mathematics of quantization of systems (involving both finitely and infinitely many degrees of freedom) with complicated geometry of phase space; (2) To study the non-commutative geometric principles underlying the physics of the microworld, and in particular possible implications for quantum gravity; (3) To explore new mathematical phenomena relating analysis to other fields of mathematics. Non-commutative geometry is a new direction of mathematics created in the eighties. Its prime objective is to study objects, called non-commutative spaces or manifolds, which are not ordinary geometric objects but still have a geometric flavor. Examples of structures of this sort arise naturally e.g. in physical theories of subatomic phenomena. Methods of non-commutative geometry became a powerful tool in studying various problems in modern analysis and understanding the fundamentals of the physics of the microworld. It is proposed to study examples of non-commutative manifolds with emphasis put on applications to quantum physics. Also, it is proposed to relate some of the ideas of quantum theory to problems in number theory and modern analysis. ***