Relativistic action at a distance through singular Lagrangians with multiplicative potentials and its relation to the nonrelativistic two-body problem

Recent models of relativistic action at a distance through singular Lagrangians with multiplicative potentials, describing two-point bound states, are re-examined. They are reformulated in such a way to be well suited to the study of extended bodies; we introduce a set of vierbeins, attached to the barycentric co-ordinates, which connect the Minkowski space with an inner relative space, and we define new relative co-ordinates in it. By using the irreducible representation theory of the Poincare group, we show that this relative space is the natural relativistic generalization of the nonrelativistic relative one. The nonrelativistic limit of these models is exhibited, by recovering the Newtonian two-body problem with central forces.