Exact parapositroniumlike solution to two-body Dirac equations

Recently we used a supersymmetric version of Dirac's constraint mechanics to derive coupled Dirac equations for a quark and antiquark in mutual chromodynamiclike interaction. Here we investigate the properties of our equations for two spinning particles in mutual electromagneticlike interaction. In the chiral Dirac matrix representation we explicitly obtain a family of exact 16-component solutions with closed-form energy spectrum that agrees with that of parapositronium through order α4. We also find that various rearrangements of our Dirac equations simultaneously yield (for weak potentials) the relativistic wave equations of Todorov and Pilkuhn as well as (for weak potentials and slow motion) the semirelativistic interaction structure of Breit