  Motivated by ultra-high-energy cosmic ray physics, we discuss all the
possible alternatives to the familiar Lorentz transformations of the momentum
and the energy of a particle. Starting from natural physical requirements, we
exclude all the possibilities, apart from the ones which arise from the usual
four-vector transformations by means of a change of coordinates in the
mass-shell. This result confirms the remark, given in a preceding paper, that,
in a theory without preferred inertial frames, one can always define a linearly
transforming energy parameter to which the GZK cutoff argument can be applied.
We also discuss the connections between the conservation and the transformation
properties of energy-momentum and the relation between energy-momentum and
velocity.
