General amplitude of the n - vertex one-loop process in a strong magnetic field

A general analysis of the n-vertex loop amplitude in a strong magnetic field is performed, based on the asymptotic form of the electron propagator in the field. As an example, the photon-neutrino processes are considered, where one vertex in the amplitude is of a general type, and the other vertices are of the vector type. It is shown, that for odd numbers of vertices only the SV_1 ... V_{n-1} amplitude grows linearly with the magnetic field strength, while for even numbers of vertices the linear growth takes place only in the amplitudes PV_1 ... V_{n-1}, VV_1 ... V_{n-1} and AV_1 ... V_{n-1}. The general expressions for the amplitudes of the processes gamma gamma -> nu bar nu (in the framework of the model with the effective nu nu e e - coupling of a scalar type) and gamma gamma -> nu bar nu gamma (in the framework of the Standard Model) for arbitrary energies of particles are obtained. A comparison with existing results is performed.