The locally-constant field approximation (LCFA) is a very useful tool in strong-field QED as it allows to compute processes in arbitrary electromagnetic fields under the condition that the classical nonlinearity parameter is large. After discussing the physical conditions behind the applicability of the LCFA I will focus on the possibility (within the LCFA) of obtaining electron and photon states in a strong plane wave by taking into the fact that these states are unstable [1]. Then, I will show how the obtained states can be used to compute probabilities of basic strong-field QED processes, which remain smaller than unity correctly accounting for the unitarity of QED [2]. Finally, I will briefly discuss our efforts to determine ultrarelativistic electron states in the presence of tightly- focused laser beams and how the tight focusing of the beam can significantly affect strong-field QED processes [3–5].
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