Interaction anomalies and one-particle dynamics for very special relativity theories

It is well known that relativistic invariance introduce strong constraints in the interactions of classical particles. We generalise the non-interaction theorems for Lorentz violating systems which still preserve a maximal subgroup of the Poincaré group. In particular, we analyse 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.