Conservation laws in “doubly special relativity”

Simon Judes and Matt Visser
Phys. Rev. D 68, 045001 – Published 4 August 2003
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Abstract

Motivated by various theoretical arguments that the Planck energy (EPlanck1019GeV) should herald departures from Lorentz invariance, and the possibility of testing these expectations in the not too distant future, two so-called “doubly special relativity” theories have been suggested—the first by Amelino-Camelia (DSR1) and the second by Smolin and Magueijo (DSR2). These theories contain two fundamental scales—the speed of light and an energy usually taken to be EPlanck. The symmetry group is still the Lorentz group, but in both cases acting nonlinearly on the energy-momentum sector. Since energy and momentum are no longer additive quantities, finding their values for composite systems (and hence finding appropriate conservation laws) is a nontrivial matter. Ultimately it is these possible deviations from simple linearly realized relativistic kinematics that provide the most promising observational signal for empirically testing these models. Various investigations have narrowed the conservation laws down to two possibilities per DSR theory. We derive unique exact results for the energy momentum of composite systems in both DSR1 and DSR2, and indicate the general strategy for arbitrary nonlinear realizations of the Lorentz group.

  • Received 22 May 2002

DOI:https://doi.org/10.1103/PhysRevD.68.045001

©2003 American Physical Society

Authors & Affiliations

Simon Judes*

  • Columbia University, New York, New York 10027, USA

Matt Visser

  • School of Mathematical and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand

  • *Electronic address: judes@physics.columbia.edu
  • Electronic address: matt.visser@vuw.ac.nz

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Vol. 68, Iss. 4 — 15 August 2003

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