Application of the new fermion-antifermion equation to positronium and the numerical solution of its static-interaction limit, the Breit equation

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Abstract
The fermion-antifermion equation derived recently is applied here to positronium with the aim of laying the groundwork for a systematic calculation of the higher-order corrections. An equation valid to the fourth order in the fine-structure constant is obtained which is equivalent to the corresponding equation derived within the Bethe-Salpeter formalism. The static-interaction limit of this equation, the Breit equation, is then decomposed into angular momentum states, whereby four second-order differential equations are obtained. The resulting eigenvalue equations are solved numerically using the appropriate boundary conditions at the origin. The resulting spectrum is in agreement with perturbative calculations.