Noncommutative geometry and applications

非对易几何是数学研究的一个新领域，起源于量子力学。这一理论的主要特点是，它涉及的对象的几何和拓扑方面，我们进行测量或执行操作或观察的顺序与结果有关。这种情况发生在微观系统，特别是那些在原子或亚原子长度尺度。这些方法已经在凝聚态物理、弦理论、随机介质、代数结构以及流形的几何和拓扑中得到了应用

Noncommutative geometry is a new field of mathematical research having its origins in quantum mechanics. The main feature of this theory is that it deals with geoemtric and topological aspects of objects for which the order in which we make measurements or perform operations or observations is relevant to the outcome. This happens with microscopic systems especially those at the atomic or subatomic length scale. The methods have been motivated by and found application in condensed matter physics, string theory, random media, algebraic structures and the geometry and topology of manifolds