Doubly special relativity theories as different bases of κ-Poincaré algebra

By Jerzy Kowalski-Glikman, S. Nowak. 2002

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Abstract Doubly Special Relativity (DSR) theory is a theory with two observer-independent scales, of velocity and mass (or length). Such a theory has been proposed by Amelino-Camelia as a kinematic structure which may underline quantum theory of relativity. Recently another theory of this kind has been proposed by Magueijo and Smolin. In this Letter we show that both these theories can be understood as particular bases of the κ -Poincare theory based on quantum (Hopf) algebra. This observation makes it possible to construct the space–time sector of Magueijo and Smolin DSR. We also show how this construction can be extended to the whole class of DSRs. It turns out that for all such theories the structure of space–time commutators is the same. This results lead us to the claim that physical predictions of properly defined DSR theory should be independent of the choice of basis.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6686909f5b9b1767fbb19e814e7506922128a97f

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, methodology): “[58, 55, 349, 140, 386, 387, 354, 388, 352, 353, 350, 26, 200, 493, 465, 291, 314, 366] and references therein), but for the purposes of this review I shall limit my consideration of DSR ideas on phenomenology to a single one of the (many) relevant issues, which is an observation that concerns the c”
Doubly special relativity and de Sitter space (2003, unknown): “Such investigations have been undertaken in [16], [17] and the results of these papers can be summarized as follows:”
Introduction to doubly special relativity (2004, background): “(See [ 19 , 21], where the relation of the DSR algebra in classical basis and Snyder’s theory is analyzed in details.) 144 J. Kowalski-Glikman”