We review recent applications of the Two Body Dirac equations of constraint
dynamics to meson spectroscopy and describe new extensions to three-body
problems in their use in the study of baryon spectroscopy. We outline unique
aspects of these equations for QED bound states that distinguish them among the
various other approaches to the relativistic two body problem. Finally we
discuss recent theorectial solutions of new peculiar bound states for
positronium arising from the Two Body Dirac equations of constraint dynamics,
assuming point particles for the electron and the positron.Comment: Invited talk: CST-MISC joint international symposium on particle
physics - From spacetime dynamics to phenomenology - Tokyo, March 15-16, 201
