Constraint dynamics of particle world lines

The Dirac generator fomulations for relativistic Hamiltonian dynamics is extended by explicitly separating the question of dynamical evolution in an inertial frame from that of changes of frame. We obtain a new elevengenerator formalism: ten to realize the Poincar\'e Lie algebra, and one to provide equations of motion. For point-particle systems, a new form of the world-line conditions is developed. It is demonstrated that with these extensions one can consistently describe classical point particles with interaction in a relativistically invariant way while maintaining invariant world lines. This paper uses the approach based on independent particle variables to set up such theories.