Reduction of the Bethe-Salpeter equation to an equivalent Schroedinger equation, with applications

We propose a new relativistic two-body formalism which reduces to a nonrelativistic Schroedinger theory for a single effective particle. The formalism is equal in rigor to that of Bethe and Salpeter, and considerably simpler to apply. We illustrate its use by computing O (α6) terms in the ground-state splitting of muonium and positronium involving infinite Coulomb exchange