On the formulation of initial-value problems for systems consisting of relativistic particles

We discuss questions related to the well-posedness of problems on the motion of relativistic many-body systems. For one-dimensional relativistic motion of $N$ similar charges, we prove that an ordinary Cauchy problem usual in Newton mechanics can be stated; this is done in the framework of microscopic Maxwell–Lorentz electrodynamics (including a model with self-action) or Wheeler–Feynman theory.