Relativistic kinematics beyond special relativity

In the context of departures from special relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale $M$, we derive the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that at that order the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of special relativity which is rotational invariant and that preserves the relativity principle at leading order in $1/M$.