  The formulation of relativistic two-body bound state wave equations and the
study of their relationship to quantum field theory began with work by
Eddington and Gaunt in 1928. However, the large variety of approaches attempted
in recent years shows that this problem still has no generally agreed-upon
solution. We describe here a recent approach resulting from " Two-Body Dirac
Equations" (emerging from Dirac's Relativistic Constraint Dynamics) that
satisfies many of the requirements one would demand of a treatment of the
relativistic two-body problem. We use its applications to QED bound states such
as positronium, QCD quarkonia, and the nucleon-nucleon scattering problem to
demonstrate the advantages of the approach.
