Abstract
Relativistic formulae for the energy level shifts due to electron self-energy corrections are derived within the external potential Bethe-Salpeter formalism. A rigorous treatment of QED corrections to the fine structure splittings of helium is carried out. Although some individual self-energy diagrams give contributions of order alpha 6mc2, they are shown to sum to zero. In addition, the alpha 6mc2 correction from vertex modifications in the presence of Coulomb photons does not contribute. Therefore, a rigorous treatment of all QED corrections of order alpha 6mc2 to the fine structure splittings of helium now appears to be complete.