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Fate of Lorentz symmetry in relative-locality momentum spaces

Giovanni Amelino-Camelia

  • Dipartimento di Fisica, Università “La Sapienza”, P.le Moro 2, Roma, Italy and INFN, Sezione Roma1, Piazzale Moro 2, 00185 Roma, Italy

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Phys. Rev. D 85, 084034 – Published 24 April, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.084034

Abstract

The most studied doubly special-relativity scenarios, theories with both the speed-of-light scale and a length/inverse-momentum scale as nontrivial relativistic invariants, have concerned the possibility of relativistically enforcing some nonlinear laws on momentum space. For the recently proposed “relative-locality framework” a central role is played by nonlinear laws on momentum space, with the guiding principle that they should provide a characterization of the geometry of momentum space. Building on previous doubly special-relativity results, here I identify a requirement necessary for “DSR compatibility”; i.e. when the requirement is not satisfied a preferred-frame formulation of theories on that momentum space inevitably emerges. I find that, within a natural parametrization of momentum-space geometry, the requirement takes the form of an elementary algorithm. By working out a few examples I provide evidence that my requirement might be not only necessary but also sufficient: when the requirement is satisfied one does manage to produce a relativistic formulation. The examples I use to illustrate the applicability of my criterion also have some intrinsic interest, including two particularly noteworthy cases of κ-Poincaré-inspired momentum spaces.

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Phys. Rev. D 85, 084034– Published 24 April, 2012
  • Received 2 November 2011

© 2012 American Physical Society

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