Unstable states in QED of strong magnetic fields.

We question the use of stable asymptotic scattering states in QED of strong magnetic elds. To correctly describe excited Landau states and photons above the pair creation threshold the asymptotic elds are chosen as generalized Licht elds. In this way the o -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 eld 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.