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arXiv · hep-th/0312227

On kappa-deformed D=4 quantum conformal group

P. Kosiński·J. Lukierski·P. Maślanka
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Abstract

This paper is presented on the occasion of 60-th birthday of Jose Adolfo de Azcarraga who in his very rich scientific curriculum vitae has also a chapter devoted to studies of quantum-deformed symmetries, in particular deformations of relativistic and Galilean space-time symmetries [1-4]. In this paper we provide new steps toward describing the $κ$-deformed D=4 conformal group transformations. We consider the quantization of D=4 conformal group with dimensionful deformation parameter $κ$. Firstly we discuss the noncommutativity following from the Lie-Poisson structure described by the light-cone $κ$-Poincaré $r$-matrix. We present complete set of D=4 conformal Lie-Poisson brackets and discuss their quantization. Further we define the light-cone $κ$-Poincaré quantum $R$-matrix in O(4,2) vector representation and discuss the inclusion of noncommutative conformal translations into the framework of $κ$-deformed conformal quantum group. The problem with real structure of $κ$-deformed conformal group is pointed out.

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P. Kosiński, J. Lukierski, P. Maślanka. 2003-12-29. On kappa-deformed D=4 quantum conformal group. https://arxiv.org/abs/hep-th/0312227

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