LOGARITHMIC CORRECTIONS IN THE BOUND-STATES PROBLEM OF QUANTUM ELECTRODYNAMICS

The logarithmic part of the Lamb shift, i. e., the contribution of the relative order alpha3 log (1/alpha) into the energy of atomic states, is related to the usual infrared divergence. This fact allows to calculate easily such a correction in positronium. Logarithmic contributions of the next order are of another relativistic nature. Their calculation is reduced to the ordinary perturbation theory for the nonrelativistic Schrodinger equation. The perturbation operators have the Breit-type structure and can be found by calculating on-mass-shell diagrams. For positronium, the calculated logarithmic correction survives only in the n3S1 state and constitutes (5/24) malpha6 log(1/alpha)/n3.