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Phys. Rev. D 69, 044001 (2004) [7 pages]

2+1 gravity and doubly special relativity

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Laurent Freidel*
Perimeter Institute for Theoretical Physics, Waterloo, Canada
ENS-Lyon, Lyon, France

Jerzy Kowalski-Glikman
Institute for Theoretical Physics, University of Wrocław, Poland

Lee Smolin
Perimeter Institute for Theoretical Physics, Waterloo, Canada
Department of Physics, University of Waterloo, Waterloo, Canada

Received 21 July 2003; published 6 February 2004

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.69.044001
DOI:
10.1103/PhysRevD.69.044001
PACS:
04.90.+e, 04.60.-m, 11.30.Cp

*Electronic address: lfreidel@perimeterinstitute.ca

Electronic address: jurekk@ift.uni.wroc.pl

Electronic address: lsmolin@perimeterinstitute.ca