Two-Body Dirac Equations from Relativistic Constraint Dynamics with Applications to QED and QCD Bound-States and to N-N Scattering

The formulation of relativistic two-body bound state wave equations and their relationship to quantum field theory began with the work by Eddington and Gaunt in 1928 [1]. However, the large variety of approaches attempted in recent years shows that this problem still has no generally agreed-upon solution. Perhaps for this reason, most recent field theory books have skirted this topic. In his recent text, Steven Weinberg states [2]: “It must be said that the theory of relativistic effects and radiative corrections in bound states is not yet in satisfactory shape.” Of course, this topic is often presented as covered by the manifestly covariant Bethe-Salpeter equation obtained directly from relativistic quantum field theory. Over the years, however, many problems have turned up to impede its direct implementation, mostly related to the central role played in it by the relative time or energy[3]. These difficulties have led many authors to attempt reformulations. We describe here a recent approach resulting from ” Two-Body Dirac Equations” (emerging from Dirac’s Relativistic Constraint Dynamics) that does satisfy 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.