Non-linear quantum dynamicsin strong and short electromagnetic fields

In our contribution we give a brief overview of two widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.m.) (e.g.\ laser) wave field or generalized Breit-Wheeler process and a single a photon emission off an electron interacting with the laser pules, so-called non-linear Compton scattering. We show that at small and moderate laser field intensities the shape and duration of the pulse are very important for the probability of considered processes. However, at high intensities the multi-photon interactions of the fermions with laser field are decisive and completely determined all aspects of subthreshold $ee$ pairs and photon production