Logarithmic corrections in the two-body problem in QED

The logarithmic part of the Lamb shift, the contribution of relative order α3log(1/α) to the atomic state energy, is related to the usual infrared divergence. This fact allows one to easily calculate this correction in positronium. Logarithmic contributions of the next order, α4log(1/α), are of a different, relativisitic nature. Their calculation is reduced to ordinary perturbation theory for the nonrelativistic Schroedinger equation. The perturbation operators have the Breit-type structure and are found by evaluating free-particle diagrams. For positronium, the calculated logarithmic correction is nonzero only in n3S1, states and is equal to 5/24mα6 log(1/α)/n3. 19 refs., 9 figs