Scattering in constraint relativistic quantum dynamics

A relativistic scattering theory is developed for a covariant constraint dynamics with direct interparticle interactions. Both time-dependent and time-independent formulations are presented, the latter being a generalization of the Lippmann-Schwinger equation. For the two-body problem, we study the simple case of maximal symmetry which, equivalently, admits both single- and two-time formulations. The two-time formalism illustrates the main features of the general case of $N\ge 3$ particles. Perturbation expansions are given for the wave function and for the $S$ matrix. Their structure is similar to those in quantum field theory corresponding to skeleton diagrams.