Modification of the quasi-levels of an electron in a laser field due to radiative corrections

The mass operator of an electron in a plane wave field of arbitrary polarisation is calculated to lowest order of alpha (but exactly with respect to the external field). It is represented by a threefold integral over elementary functions or a double integral over exponential integral functions. For a monochromatic plane wave and circular polarisation the number of integrations reduces by one and the mass operator turns out to be almost diagonal. In this case the corrected propagator is obtained and the modifications of the quasi-levels of the electron are investigated. The property of the mass operator and the propagator of being almost diagonal is related to a special symmetry of the circularly polarised field and found to be valid to all orders.