Interaction anomalies and one-particle dynamics for maximal relativity subgroups

It is well known that relativistic invariance introduceds strong constraints in the interactions of classical particles. We generalize the non-interaction theorems for Lorentz violating systems which still preserve a maximal subgroup of the Poincaré group. In particular, we analyze the motion of a particle preserving the very special relativity symmetry introduced by Cohen and Glashow. We also discuss the case of the homogeneous subgroup. We extend the analysis for Galilei invariant multiparticle systems and for the dynamics of a particle symmetric under any maximal subgroup of Galilei group, including the homogeneous subgroup.