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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.
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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 of de Sitter, anti-de Sitter, and flat space, respectively.
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 relativistic limit of small wave-vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the $(omega,k)$ space, with an additional invariant given by the wave-vector $k=pi /2$. The space-time reconstructed from the $(omega,k)$ space is intrinsically quantum, and exhibits the phenomenon of relative locality.
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 masses, the higher their corresponding Z resonance energy peaks. A twin light neutrino mass splitting may reflect into a twin Z resonance and a complex UHECR spectra modulation as a twin bump at at highest GZK energy cut-off. Each possible neutrino mass associates a characteristic dark halo size (galactic, local, super cluster) and its anisotropy due to our peculiar position within that dark matter distribution. The expected Z or WW,ZZ showering into proton-anti proton and neutron-anti neutron might correspond to peculiar clustering in observed UHECR at 10^{19}, 2 10^{19}, 4 10^{19} eV. A neutrino light HDM halo around a Mpc will allow to the UHECR neutron--anti-neutron secondary component at E_n> 10^{20} eV (due to Z decay) to arise playing a role comparable with the charged p-bar{p} ones. Their un-deflected n-bar{n} flight is shorter leading to a prompt and hard UHECR trace pointing toward the original UHECR source direction. The direct proton-antiproton pairs are split and spread by random magnetic fields into a more diluted and smeared and lower energy UHECR signal around the original source direction. Additional prompt TeVs signals by synchrotron radiation of electro-magnetic Z showering must also occur solving the Infrared-TeV cut-off. The observed hard doublet and triplets spectra, their time and space clustering already favour the rising key role of UHECR n-bar n secondaries originated by neutrino-Z tail shower.
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 symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.
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