THE 2-BODY PLUS POTENTIAL PROBLEM BETWEEN QUANTUM-FIELD THEORY AND RELATIVISTIC QUANTUM-MECHANICS (2-FERMION AND FERMION-BOSON CASES)

Starting with a pair of integrodifferential Bethe-Salpeter equations for two fermions interacting mutually and with an external static potential, we obtain a pair of compatible and separable coupled Dirac equations, between which the unwanted relative time variable can be easily eliminated. We use two different adaptations of the method proposed by Sazdjian for the two-particle (without external potential) problem, leading to two different (although equivalent) systems of coupled Dirac equations. We examine the instantaneous approximation and we test our methods in the helium atom problem. The last section is devoted to the fermion-boson plus external potential problem.