02-427 Gonzalez-Mestres, L.

Deformed Lorentz Symmetry and High-Energy Astrophysics (III) (37K, LaTeX) 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 low-energy limit (deformed Lorentz symmetry, DLS). DLS can have important implications for ultra-high energy cosmic-ray physics (see papers physics/0003080 - hereafter referred to as I - , astro-ph/0011181 and astro-ph/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 ( hep-th/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 space-time dimensions and compare our QDRK model, in the form proposed since 1997, with the Kirzhnits-Chechin (KCh) and Sato-Tati (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 Magueijo-Smolin transformation as a technical tool.

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