From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics
Abstract
We present a short review describing the use of noncommutative space-time in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and -deformed cases. Finally we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates.
Keywords
Cite
@article{arxiv.1012.3629,
title = {From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics},
author = {Jerzy Lukierski},
journal= {arXiv preprint arXiv:1012.3629},
year = {2011}
}
Comments
29 pages, 1 fig.eps. Invited talk at 50-th Cracow School of Theoretical Physics "Particle Physics at the Dawn of the LHC'', Zakopane, Poland (June 9-19, 2010). To be published in Acta Physica Polonica~B. This paper is an extended version of the text presented at First Galileo-Xu Quang-qi Meeting (Shanghai, October 2009) and published as arXiv:1003.4185 [hep-th]