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Abstract

In this thesis, radiative corrections to electron states in a background plane-wave laser field are investigated. At the tree level, electrons are described by Volkov states, which are solutions to the Dirac equation in a plane-wave field. However, the interaction of an electron with its own electromagnetic field leads to “radiative” modifications of the states. In the present work, the leading-order radiatively corrected Volkov states are derived for a linearly polarized plane-wave field by solving the Dirac-Schwinger equation perturbatively. Corrections to the phase and spinor-structure of the Volkov states are obtained to leading-order in the fine-structure constant. Both the quasi-momentum of the electron and its dressed mass are shown to be altered by quantum radiative corrections. Remarkably, it is found that the dressed mass of the electron becomes in general spin-dependent. For the case of a constant-crossed field, a new derivation of the mass operator entering the Dirac-Schwinger equation is presented. Moreover, asymptotic and convergent series for the spin-dependent part of the dressed mass are obtained in this case. The results can be used to calculate first-order loop corrections to elementary processes in intense laser fields.