Correspondence principle in the self-energy problem

Abstract

It has been shown by Fomin and the author [ Soviet Physics JETP 40 (1975), 6] that in the classical limit, h ̷ → 0 , there is a correspondence between the quantum and classical electron self-energies in spinor electrodynamics. In the present work this result is extended to the cases of scalar electrodynamics and scalar meson theory. The apparent violation of the correspondence principle in the self-energy problem, noted in the literature, can be ascribed to the inadequacy of the usual expansion procedure in terms of the parameters e 2 h ̷ c and mc Λ = mcr 0 h ̷ as h ̷ → 0 (here Λ is the usual cutoff parameter, r 0 is the cutoff radius).