Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics

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 $\kappa$-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 $\kappa$-deformed Minkowski space is provided by quantum $\kappa$-deformation of Poincaré symmetries.

LaTex, 15 pages; minor corrections of formulae (1) and (4), footnote 2 added. Journal references added

References in corpus (3)

• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Deformed Boost Transformations That Saturate at the Planck Scale
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times

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