Effects of retardation on electromagnetic self-energy of atomic states

The significance of retardation effects in photon emissions and absorptions is emphasized in the calculation of self-energy. It is explicitly demonstrated that inclusion of such effects leads to a finite answer for the shifts of atomic energy levels in a nonrelativistic theory without cutoff. Ambiguities that exist in the mass renormalization in the nonrelativistic approach are pointed out. Such ambiguities vanish from the relativistic theory. Explicit calculation is carried out in the case of hydrogen by utilizing the Coulomb Green's function. The advantage of the present approach in calculating self-energy shift in high-$Z$ hydrogenic ions is suggested.