Dispersion relations for threshold reactions in an external electromagnetic field

Nonlinear threshold phenomena in quantum systems in a strong external electromagnetic field are investigated. A development of traditional quantum electrodynamics (QED) and a modified QED with a new universal parameter, fundamental mass, are used. Analysis of the threshold phenomena in an external magnetic field is based on the modified Dirac equation in an external field. The analysis shows that the fundamental mass determines a bound on the external field strength. Dispersion relations are proved for some threshold reactions in rather general external electromagnetic fields.