Form of relativistic dynamics with world lines

In any Hamiltonian relativistic theory there are ten generators of the Poincaré group which are realized canonically. The dynamical evolution is described by a Hamiltonian which is one of the ten generators in Dirac's generator formalism. The requirement that the canonical transformations reproduce the geometrical transformation of world points generates the world-line conditions. The Dirac identification of the Hamiltonian and the world-line conditions together lead to the no-interaction theorem. Interacting relativistic theories with world-line conditions should go beyond the Dirac theory and have eleven generators. In this paper we present a constraint dynamics formalism which describes an eleven-generator theory of $N$ interacting particles using $8(N+1\mathrm{})\mathrm{}$ variables with suitable constraints. The $\mathrm{}(N+1\mathrm{})\mathrm{}\mathrm{th}$ pair of four-vectors is associated with the uniform motion of a center which coincides with the center of energy for free particles. In such theories dynamics and kinematics cannot be separated out in a simple fashion.