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Doubly Special Relativity versus $κ$-deformation of relativistic kinematics

J. Lukierski·A. Nowicki
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Abstract

We argue that recently proposed by Amelino-Camelia et all [1,2] so-called doubly special relativity (DSR), with deformed boost transformations identical with the formulae for $κ$-deformed kinematics in bicrossproduct basis is a classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed fourmomenta as advocated in [1, 2] implies that DSR is obtained by considering nonlinear fourmomenta basis of classical Poincaré algebra and it does not lead to noncommutative space-time. We also show how to construct large two classes of doubly special relativity theories - generalizing the choice in [1,2] and the one presented by Magueijo and Smolin [3]. The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative $κ$-deformed Minkowski space is provided by quantum $κ$-deformation of Poincaré symmetries.

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J. Lukierski, A. Nowicki. 2003-01-24. Doubly Special Relativity versus $κ$-deformation of relativistic kinematics. https://doi.org/10.1142/s0217751x03013600

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