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 Poincaré 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.

• Received 5 January 1981

DOI:https://doi.org/10.1103/PhysRevD.23.2218