LOGARITHMIC CORRECTIONS IN THE 2-BODY QED PROBLEM

The logarithmic part of the Lamb shift, the contribution of the relative order alpha3 log (1/alpha) to the atomic state energy, is related to the usual infrared divergence. This fact allows one to calculate easily such corrections in positronium, and derive the recoil and electron-electron terms in the Lamb-shift Hamiltonian in many-electron atoms. Logarithmic energy corrections of the next order, alpha4 log (1/alpha), are of a different, 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 are found by the calculation of on-mass-shell diagrams. For positronium, the calculated log-arithmic correction survives only in nS-3(1) states and constitutes 5/24malpha6 log (1/alpha)/n3. Logarithmic corrections of the relative order alpha2 log (1/alpha) to the positronium decay rate are also of the relativistic origin and can be easily computed within the same approach. Arguments are presented in favour of a large numerical factor in the (alpha/pi)2 correction to the positronium decay rate.