Towards a topological (dual of) quantum $κ$-Poincaré group

Details Towards a topological (dual of) quantum $κ$-Poincaré group Towards a topological (dual of) quantum $κ$-Poincaré group

2005-05-11

arxiv.org/abs/hep-th/0505093v1

Rept.Math.Phys. 57 (2006) 233-256

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 22 pages, uspackage: pstricks,pst-plot

Scientific paper

10.1016/S0034-4877(06)80019-4

We argue that the $\kappa$-deformation is related to a factorization of a Lie group, therefore {\em an approproate version of $\kappa$-Poincar\'{e} does exist on the $C^*$-algebraic level}. The explict form of this factorization is computed that leads to an ``action'' of the Lorentz group (with space reflections) considered in Doubly Special Relativity theory. The orbit structure is found and ``the momentum manifold'' is extended in a way that removes singularities of the ``action'' and results in a true action. Some global properties of this manifold are investigated

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