The relativistic two-body Coulomb system

We derive integral equations for a relativistic system of two particles, interacting via the Coulomb force, from the underlying quantum field theory. Three cases, where particles are charged spinless scalars or spin-1/2 fermions, are considered. We discuss the ground-state solutions of these equations in the perturbative and strong-coupling (high-Z) regime for arbitrary masses and charges of the particles. In the limit where the mass of one of the particles becomes infinite comparison is made with the Dirac-Coulomb and Klein-Gordon-Coulomb equations. (author)