Constraint Hamiltonian dynamics of directly interacting relativistic point particles

The author gives a demonstration of a consistent constraint-Hamiltonian formulation of relativistic many-point-particle dynamics. Some peculiarities like the dependence of interacting particles' world line on the choice of an equal-time plane, as well as the particle number independence of the scattering matrix have been discussed. Moreover, the realistic features and practical usefulness of the constraint-Hamiltonian approach have been displayed on both classical and quantum level. Finally, a section deals with some unsolved problems. (Auth./G.J.P.)