Short review on noncommutative spacetimes

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Pachol, A.^1

Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavik, Iceland^1

关键词: Basic elements;    Differential operators;    Hopf algebras;    Non-commutative;    Planck scale;    Quantum groups;    Space-time coordinates;    Twist deformations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012039/pdf
DOI  :  10.1088/1742-6596/442/1/012039

学科分类：力学，机械学

来源: IOP

【 摘 要 】

This review presents noncommutative spacetimes as one of the approaches to Planck scale physics, with the main assumption that at this energy scale spacetime becomes quantized. Spacetime coordinates become noncommutative as observables in Quantum Mechanics. The basic elements of Drinfeld twist deformation theory are reminded. The Hopf algebra language provides natural framework for deformed relativistic symmetries which constitute Quantum Group of symmetry and noncommutative spacetime is in fact Hopf module algebra. The notion of realization for noncommutative coordinates in terms of differential operators is also presented.