We consider the relativistic quantum mechanics of a two interacting fermions
system. We first present a covariant formulation of the kinematics of the
problem and give a short outline of the classical results. We then quantize the
system with a general interaction potential and deduce the explicit equations
in a spherical basis. The case of the Coulomb interaction is studied in detail
by numerical methods, solving the eigenvalue problem for J=0, J=1, J=2 and
determining the spectral curves for a varying ratio of the mass of the
interacting particles. Details of the computations, together with a
perturbative approach in the mass ratio and an extended description of the
ground states of the Para- and Orthopositronium are given in Appendix.Comment: 26 pages, 6 figure
