Relativity principle with a low energy invariant scale
  The possibility of a modification of special relativity with an invariant energy scale playing the role of a minimum energy is explored. Consistency with the equivalence of different inertial frames is obtained by an appropriate choice of a non-linear action of the Lorentz group on momentum space. Limits on the low energy cutoff from tests of Einstein's theory and possible ways to measure the new energy scale are discussed. 
Jose Manuel Carmona, Jose Luis Cortes