SINGULARITY-FREE BREIT EQUATION FROM CONSTRAINT 2-BODY DIRAC EQUATIONS

We examine the relation between two approaches to the quantum relativi stic two-body problem: (1) the Breit equation, and (2) the two-body Di rac equations derived from constraint dynamics. In applications to qua ntum electrodynamics, the former equation becomes pathological if cert ain interaction terms are not treated as perturbations. The difficulty comes from singularities which appear at finite separations r in the reduced set of coupled equations for attractive potentials even when t he potentials themselves are not singular there. They are known to giv e rise to unphysical bound states and resonances. In contrast, the two -body Dirac equations of constraint dynamics do not have these patholo gies in many nonperturbative treatments. To understand these marked di fferences we first express these contraint equations, which have an '' external potential'' form, similar to coupled one-body Dirac equations , in a hyperbolic form. These coupled equations are then recast into t wo equivalent equations: (1) a covariant Breit-like equation with pote ntials that are exponential functions of certain ''generator'' functio ns, and (2) a covariant orthogonality constraint on the relative momen tum. This reduction enables us to show in a transparent way that finit e-r singularities do not appear as long as the exponential structure i s not tampered with and the exponential generators of the interaction are themselves nonsingular for finite r. These Dirac or Breit equation s, free of the structural singularities which plague the usual Breit e quation, can then be used safely under all circumstances, encompassing numerous applications in the fields of particle, nuclear, and atomic physics which involve highly relativistic and strong binding configura tions.