AbstractIt is proposed that particle interactions can be described by means of simple group operations in non‐compact Lie groups. Prescriptions for the structure of these group operations are formulated which are motivated by the study of simple models, in particular of the dynamics of the hydrogen atom. If they are fulfilled we call the structure “group dynamics”.Neglecting at first internal symmetries, a few simple models are investigated in which group dynamics is possible. The groupO(3,1) turns out to describe the coupling of pseudoscalar mesons,O(4,2) that of photons to baryons quite well: The pionic decay rates of baryon resonances up to spin 19/2 and the electromagnetic form factors of the nucleons are predicted in good agreement with experiment.The internal symmetrySU(3) is included in theO(3.1) model of the pionic coupling in the simplest way, by assumingO(3,1) ×SU(3) to be the dynamical group. This gives rise to a minimal symmetry breaking of the amplitudes and relates it to the mass differences inSU(3) multiplets: The amplitude consists of a product of aSU(3) Clebsch Gordan coefficient and a universal function of the velocity of the final baryon. The way the particle masses enter the decay rates is uniquely prescribed in this approach. The agreement with experiment is excellent.Finally, the connection of this purely algebraic approach with related ideas, like the use of infinite component wave equations, is dis