Classical mechanics of directly interacting relativistic particles

Abstract

We discuss the classical mechanics of relativistic systems containing any number of particles with direct interaction. We continue our previous approach of restricting the observables to gauge invariant variables. As a preliminary we show how to constructN-particle mass shell constraints. Physical momentum and position variables are constructed in consonance with nonsuperluminality and relativity and consistent with a slightly weakened separability which allows the position four vector of separated particles to differ from the canonical coordinate four vector by a constant term which depends on its history but does not affect future dynamics. The formalism is mathematically consistent though slightly more complicated than previous attempts in this direction.