Bound state QED effects from the Schrödinger equation

Abstract

We present a new relativistic bound-state formalism for two interacting Fermi–Dirac particles. The kernel of the integral equation for the bound-state system is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. The method is illustrated through calculations of the hyperfine and fine splittings of positronium up to order α5. Our calculations of the one-loop contributions are carried out in the explicitly covariant Feynman gauge. We also present new results for the hyperfine and fine splittings in positronium to order α5 for arbitrary principal quantum number n, which are easily obtained owing to the virtue of conceptual and calculational simplicity of our formalism. In addition, we present the one-loop renormalization scheme in our formalism.