Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-03-07
Int.J.Mod.Phys. A18 (2003) 7-18
Physics
High Energy Physics
High Energy Physics - Theory
LaTex, 15 pages; minor corrections of formulae (1) and (4), footnote 2 added. Journal references added
Scientific paper
10.1142/S0217751X03013600
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 Poincar\'{e} 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 Poincar\'e symmetries.
Lukierski Jerzy
Nowicki Anatol
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