Unstable states in QED of strong magnetic fields

We question the use of stable asymptotic scattering states in QED of strong magnetic fields. To correctly describe excited Landau states and photons above the pair creation threshold the asymptotic fields are chosen as generalized Licht fields. In this way the off-shell behavior of unstable particles is automatically taken into account, and the resonant divergences that occur in scattering cross sections in the presence of a strong external magnetic field are avoided. While in a limiting case the conventional electron propagator with Breit-Wigner form is obtained, in this formalism it is also possible to calculate $S$-matrix elements with external unstable particles.