The Principles of Quantum Mechanics and of Classical General Relativity indicate that Spacetime in the small (Planck scale) ought to be described by a noncommutative C* Algebra, implementing spacetime uncertainty relations. A model C* algebra of Quantum Spacetime and its Quantum Geometry is described. Interacting Quantum Field Theory on such a background is discussed, with open problems and recent progress. Applications to cosmology suggest that the Planck scale ought to depend upon dynamics, and possible consequences in the large of the quantum structure in the small are outlined.

中文翻译：

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量子时空，量子几何和普朗克标度

量子力学原理和经典广义相对论表明，小时空（普朗克尺度）应该由非交换C *代数描述，并实现时空不确定性关系。描述了量子时空的模型C *代数及其量子几何。在这样的背景下讨论了相互作用量子场论，存在开放性问题和最新进展。在宇宙学上的应用表明，普朗克尺度应取决于动力学，并概述了量子结构中小分子可能产生的后果。