Slow motion approximation in predictive relativistic mechanics. II. A noninteraction theorem for interactions derived from the classical field theory

By adopting an Aristotle invariant Lagrangian formalism (equivalent to canonically representing only this subgroup of the Poincaré group) and imposing a certain separability condition and a Newtonian limit on the Lagrangian, we obtain the most general Lagrangian up to c−3 order that verifies these properties and leads to a relativistic invariant dynamic (i.e., it satisfies the Currie–Hill equations). It contains up to c−2 order, all the Lagrangians known up to the present time. It is shown that the interactions derived from the classical field theory (CFT) do not admit approximated Lagrangians up to c−4 order, and thus this constitutes a noninteraction theorem for said interactions and somehow justifies some authors’ attitudes of abandoning the Lagrangian formalism (dropping the canonical character of position coordinates) when they construct a Hamiltonian formalism for these systems.