Infrared and collinear divergences in gauge theories

The problem of infrared and collinear divergences is considered within the framework of perturbation theory and the scattering operator redefinition method. IR divergent processes in electrodynamics and gravitation (perturbation theory) are described, and for the case of electrodynamics a scattering operator free from IR divergences is constructed. For the massless electrodynamics model, a recipe for constructing a scattering operator free from both IR and collinear divergences is given. The meaning of experimental parameters entering the final formulas is discussed, and it is shown that the S-matrix factorization (i.e., the approximate independence of hard and soft processes) makes the theorem on the cancellation of divergences in observables trivial. A method for finding divergences in theories with multiparticle vertices is presented.