Renormalization Constants, Wave Functions, and Energy Shifts in the Coulomb and Lorentz Gauges

Abstract

The scattering wave functions for quantum electrodynamics are examined in the Coulomb gauge, in the conventional Lorentz gauge, and in a reformulated version of the Lorentz gauge. It is shown that when the Lorentz gauge is formulated so that Maxwell's equations hold even when the Green's-function pole is displaced off the real axis, ${Z}_{2}$ is identical in the Coulomb gauge and in the Lorentz gauge. It is also shown that the unrenormalized asymptotic states in the reformulated Lorentz gauge include a partial dressing of the bare electrons by longitudinal and timelike photons sufficient to generate the electron's static electric field. It is proven that for true bound states the radiative energy shifts in the reformulated Lorentz gauge and in the conventional formulation agree.