Research on infrared divergence reduction for scattering problems in external electromagnetic fields

Abstract

In field theory, there exist two types of divergence: The first is ultraviolet divergence that occurs in the momentum region of large virtual particles in the inner line of the Feynman diagram. The second is infrared divergence that occurs in the momentum region of small real and virtual particles. To eliminate ultraviolet divergence, there are 3 methods: Pauli-Vallars method, dimension adjustment method, large momentum cutting method. To eliminate infrared divergence, the lmin method is used. In this article, we study the application of correction methods of ultraviolet divergence to infrared divergence and discuss the relationship between the two above methods. Calculate the scattering amplitude and its correction for the problem of electron scattering in the external field.