Anomalous dimension and infrared behaviour for high energy QED

The generalization of the Sudakov results for real photons is obtained. It allows one to calculate the anomalous dimensions for the Coulomb and the electron-electron scattering. The formulas ΔE=Eexp(-eta(E/m)) for the Coulomb case and ΔE=√sexp(-eta(s/m2)) for the electron-electron case are given. These formulas give anomalous dimensions which depend on the energy. This dependence, which comes from the Sudakov double logarithmic behaviour of QED, disappears for semi-inclusive scattering. These These results can be extended to other models of QFT like scalar QED or QCD and they partially justify the eikonal approximation. (author)