Analytic bound-state solutions in a relativistic two-body formalism with applications in muonium and positronium

This work advocates the use in atomic physics of a new relativistic two-body formalism equal in rigor to the Bethe-Salpeter formalism and clearly superior to it in several respects. Outstanding among these is the existence of a Coulomb-like kernel for which the exact analytic solutions of the bound-state equations are known. These solutions are derived and applied in a calculation of the $O\left({\alpha }^{6}m\ln {\alpha }^{-1\mathrm{}}\right)$ contributions to hfs in muonium and positronium. Three previously unknown contributions are found. Theory and experiment are compared.