This work provides an overview of our recent results in studying two mostimportant and widely discussed quantum processes: electron-positron pairsproduction off a probe photon propagating through a polarized short-pulsedelectromagnetic (e.g.\ laser) wave field or generalized Breit-Wheeler process,and a single a photon emission off an electron interacting with the laserpules, so-called non-linear Compton scattering. We show that the probabilitiesof particle production in both processes are determined by interplay of twodynamical effects, where the first one is related to the shape and duration ofthe pulse and the second one is non-linear dynamics of the interaction ofcharged fermions with a strong electromagnetic field. We elaborate suitableexpressions for the production probabilities and cross sections, convenient forstudying evolution of the plasma in presence of strong electromagnetic fields
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