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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 κ\kappa-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 κ\kappa-Minkowski space. Furthermore, we give an explicit realization of the action of the κ\kappa-Poincar\'e algebra as an involutive Hopf algebra on this representation of κ\kappa-Minkowski space and initiate a study of its properties.

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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