标题： 非交换几何方法对时空量子结构的研究 显示英文标题

标题： A noncommutative geometric approach to the quantum structure of spacetime

摘要： 与合作者一起，我们在过去几年里引入了定义在Moyal代数上的非交换黎曼几何，并系统地将其发展到嵌入高维空间的非交换空间上。 该理论被应用于构造广义相对论的非交换版本，期望能够捕捉时空在普朗克尺度下的一些本质结构特征。 详细研究了一些非交换时空的例子，包括平面引力波、量子史瓦西时空和史瓦西-德西特时空的量子化，以及一个与引力坍缩相关的量子托尔曼时空。 在这里我们简要回顾这一理论及其在研究时空量子结构中的应用。 显示英文摘要

摘要： Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to construct a noncommutative version of general relativity, which is expected to capture some essential structural features of spacetime at the Planck scale. Examples of noncommutative spacetimes were investigated in detail. These include quantisations of plane-fronted gravitational waves, quantum Schwarzschild spacetime and Schwarzschild-de Sitter spacetime, and a quantun Tolman spacetime which is relevant to gravitational collapse. Here we briefly review the theory and its application in the study of quantum structure of spacetime.