Internal Structure of Ultra-High Energy Particles with Lorentz Symmetry   Violation at the Planck Scale
  Assuming the existence of a local vacuum rest frame (LVRF), and using suitable algebraic tranformations, the internal structure of ultra-high energy particles (UHEPs) is studied in the presence of Lorentz symmetry violation (LSV) at the Planck scale. Violations of the standard Lorentz contraction and time dilation formulae are made explicit. Dynamics in the rest frame of a UHEP is worked out and discussed. Phenomenological implications for ultra-high energy cosmic rays (UHECR), including possible violations of the Greisen-Zatsepin-Kuzmin GZK) cutoff, are studied for several LSV models. 
Luis Gonzalez-Mestres