On Dirac’s theory of quantum electrodynamics: the interaction of an electron and a radiation field

Abstract

The paper considers the interaction of an electron with a radiation field in the higher approximations. Denoting by ψ n that part of the wave function which involves the n th power of the charge e and by ψ n.m that part of ψ n which refers to m photons, it is found that for a general solution ψ 0 , ψ 1 , ψ 2 , ψ 3 are all finite and ψ 4 has finite parts ψ 4.4 and ψ 4.2 but divergent ψ 4,0 . For the particular solution which corresponds to outgoing waves of the electron, all divergent integrals disappear. ψ n.m is zero for all m different from n , and the value of ψ n.m can be written down easily. The solution makes it now possible to consider exactly processes involving any number of photons, whereas previously exact calculations had to be confined to at most two photons.