 02427 GonzalezMestres, L.
 Deformed Lorentz Symmetry and HighEnergy Astrophysics (III)
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Oct 17, 02

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Abstract. Lorentz symmetry violation (LSV) can be generated at the Planck scale, or
at some other fundamental length scale, and naturally preserve Lorentz
symmetry as a lowenergy limit (deformed Lorentz symmetry, DLS). DLS can
have important implications for ultrahigh energy cosmicray physics (see
papers physics/0003080  hereafter referred to as I  , astroph/0011181
and astroph/0011182, and references quoted in these papers). A crucial
question is how DLS can be extended to a deformed Poincar\'e symmetry
(DPS), and w hat can be the dynamical origin of this phenomenon. In a
recent paper ( hepth/020 8064 , hereafter referred to as II), we started
a discussion of proposals to identify DPS with a symmetry incorporating
the Planck scale (like doubly special relati vity, DSR) and suggested new
ways in similar directions. Implications for models of quadratically
deformed relativistic kinematics (QDRK) and linearly deformed rela
tivistic kinematics (LDRK) were also discussed. We pursue here our study
of these basic problems, focusing on the possibility to relate deformed
relativistic kinematics (DRK) to new spacetime dimensions and compare
our QDRK model, in the form proposed since 1997, with the KirzhnitsChechin
(KCh) and SatoTati (ST) models. It is pointed out that, although the KCh
model does not seem to work such as it was formulated, our more recent
proposals can be related to suitable extensions of this model generalizing
the KCh finslerian pattern (even to situations where a preferr ed physical
inertial frame exists) and using the MagueijoSmolin transformation as
a technical tool.
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