Renormalization-group analysis of photon processes in an external field

It is noted that renormalization-group analysis can be applied to the investigation of the asymptotic behavior of amplitudes with respect to any dimensional parameter. As an illustration, the Callan–Symanzik equation is used to analyze the asymptotic behavior of the photon vertices of quantum electrodynamics with respect to a strong constant external field. Considered in detail is the amplitude for splitting of one photon into two for the cases of a magnetic field and a crossed field and the regions of low and high photon energies. The consequences of the finite charge renormalization hypothesis (ultraviolet-stable zero of the Callan–Symanzik function) are discussed from the point of view of the behavior of the photon vertices in the strong-field limit.