Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field

Abstract

An intuitive explanation is given for the electromagnetic shift of energy levels by calculating the mean square amplitude of oscillation of an electron coupled to the zero-point fluctuations of the electromagnetic field. The resulting disturbance of the charge and current density of the electron gives rise to various observable effects which can be estimated in a simple classical fashion. The effects treated are the Lamb shift, the correction to the $g$-factor for the orbital and spin angular momenta of the electron, and the correction to the Compton scattering cross section at low energies. A simple explanation is also given for the peculiar ultraviolet divergence noticed by Pauli and Fierz in their treatment of the infra-red paradox.