Generalized Lorentz invariance with an invariant energy scale

João Magueijo and Lee Smolin
Phys. Rev. D 67, 044017 – Published 27 February 2003
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Abstract

The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultrahigh-energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.

  • Received 22 July 2002

DOI:https://doi.org/10.1103/PhysRevD.67.044017

©2003 American Physical Society

Authors & Affiliations

João Magueijo

  • Theoretical Physics, The Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, United Kingdom

Lee Smolin

  • Perimeter Institute for Theoretical Physics, Waterloo, Canada N2J 2W9
  • Department of Physics, University of Waterloo, Waterloo, Canada N2J 2W9

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Issue

Vol. 67, Iss. 4 — 15 February 2003

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