We propose a new relativistic two-body formalism which reduces to a nonrelativistic Schr\"odinger 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.
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Caswell et al. (1978) studied this question.