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Should projects of space experiments on ultra-high energy cosmic rays be supported, whatever AUGER results will turn out to be? We claim that this is indeed the case. It is now widely admitted that models of Lorentz symmetry violation (LSV) at the Planck scale based on power-like extrapolations down to cosmic-ray scales and able to account for a possible absence of the Greisen-Zatsepin-Kuzmin cutoff exist and require the existence of a privileged inertial rest frame, as we proposed in 1997 (paper physics/9704017 and subsequent work). The favoured energy dependence of the LSV parameter will then be quadratic rather than linear. This approach (weak doubly special relativity, WDSR) is different from the version of doubly special relativity defended by several authors, where the laws of Physics are required to be exactly identical in all inertial reference frames (strong doubly special relativity, SDSR). To date, WDSR patterns based on a deformation of special relativity with a privileged (vacuum) rest frame are the only clear and consistent candidate to explain a possible absence of the GZK cutoff invoking deviations from standard relativity. It is also to be emphasized, as in hep-ph/0510361, that the usual hypothesis of a power-like dependence of the LSV effective parameters not being altered by any intermediate energy scale is not the only possible one. Therefore, experiments sensitive to UHCR energies as high as possible become necessary irrespective of AUGER results.
We show that depending on the direction of deformation of $kappa$-Poincare algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form
It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac evolution in the
The current status of Doubly Special Relativity research program is shortly presented. I dedicate this paper to my teacher and friend Professor Jerzy Lukierski on occasion of his seventieth birthday.
The Ultra High Energy Cosmic Ray (UHECR), by UHE neutrino-relic neutrino--Z showering in Hot Dark Halos (HDM), shows an energy spectra, an anisotropy following the relic neutrino masses and clustering in dark halo. The lighter are the relic neutrinos
In this paper we recall the construction of scalar field action on $kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $kappa$-Poincare algebra of symmetries arises from the analysis of the symmetr