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Abstract

The primary aim of this thesis is to advance the understanding of higher-order laser-assisted relativistic processes within quantum electrodynamics (QED), which necessitates a formulation using fully laser-dressed fermion propagators. This study is motivated by presently available laser sources which routinely produce electromagnetic fields strong enough to accelerate the electron to velocities close to the speed of light. The strong laser-matter interaction requires an all-order treatment, different from the perturbative expansion of the usual QED. In this thesis, the influence of a strong laser field on two fundamental processes of QED is studied theoretically. The first process, bremsstrahlung from an electron scattered at the Coulomb potential of a nucleus, is found to show a resonant behavior in the presence of the laser. The cross section is numerically evaluated from the formula resulting from applying the strong-field Feynman rules. The second process, electron-positron pair creation by a gamma photon and a Coulomb field is studied in the case when the laser field strength is below the critical field. Here the total cross section is unchanged by the laser, while the differential cross section is drastically modified. Finally, a detailed study and a novel evaluation algorithm of the generalized Bessel function, a special function occurring naturally in laser-modified QED, is presented.