Formulation of the relativistic mechanics of systems of interacting particles

A Poincaré invariant formulation of classical relativistic mechanics of a system of $n$ interacting particles is given. The equations of motion are the equations of the characteristics of a Pfaffian form, which relates the action element to the elements of the $4n$ coordinates of the system. The characteristics are found on a subsurface defined by $n$ constraints, which include the particle masses. A canonical transformation to collective variables for two particles is found, this satisfying the conditions of covarianee and the correct nonrelativistic limit. The action satisfies $n$ Hamilton–Jacobi equations. The scattering of two particles is considered. The nonuniqueness of the worldlines of the particles in the interaction region is discussed.