We propose a new relativistic two-body formalism which reduces to a nonrelativistic Schrödinger 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 $O\left({\alpha }^6\right)$ terms in the ground-state splitting of muonium and positronium involving infinite Coulomb exchange.

• Received 10 February 1978

DOI:https://doi.org/10.1103/PhysRevA.18.810