Relativistically interacting particles and world lines

The action of the Poincaré group $P$ on the phase space $\Gamma$ of two interacting relativistic particles is studied. Trajectories are defined by introducing two fixation constraints which, together with two first-class dynamical constraints, form a second-class system. By a projection followed by an injection, a pair of world lines are defined in Minkowski space. A world-line condition is determined by the commutation of the Poincaré transformation with the projection-injection map. The results are compared with those of our preceding paper.