Complete description of polarization effects in the nonlinear Compton scattering. I. Circularly polarized laser photons

We consider emission of a photon by an electron in the field of a strong laser wave. Polarization effects in this process are important for a number of physical problems. We discuss a probability of this process for circularly polarized laser photons and for arbitrary polarization of all other particles. We obtain the complete set of functions which describe such a probability in a compact covariant form. Besides, we discuss an application of the obtained formulas to the problem of electron -> photon conversion at photon-photon and photon-electron colliders.