Star product realizations of kappa-Minkowski space
Mathematical Physics
2013-11-21 v1 High Energy Physics - Theory
Functional Analysis
math.MP
Quantum Algebra
Abstract
We define a family of star products and involutions associated with -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on -Minkowski space. Furthermore, we give an explicit realization of the action of the -Poincar\'e algebra as an involutive Hopf algebra on this representation of -Minkowski space and initiate a study of its properties.
Keywords
Cite
@article{arxiv.1104.0206,
title = {Star product realizations of kappa-Minkowski space},
author = {Bergfinnur Durhuus and Andrzej Sitarz},
journal= {arXiv preprint arXiv:1104.0206},
year = {2013}
}
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35 Pages