The effect of damping on radiative corrections to electron scattering and the problem of infra-red catastrophe

Abstract

The reaction of radiation on the scattering of electrons with radiative corrections is treated on the basis of covariant theory of radiation damping. It is shown that the ultra-violet divergences are removed by the process of usual mass and charge renormalisations; and the infra-red divergence, which still persists in the second order corrections to radiationless electron scattering is exactly compensated by the corresponding divergence occurring in the scattering with the emission of radiation. In §1 the interaction Hamiltonian for the scattering processes are given after Feynman-Dyson formalism. In §2 the covariant formulation of radiation damping and the scattering cross-sections are given. The §3 deals with the infra-red divergences involved in the electron scattering.