Quantum electrodynamics and radiation reaction: Nonrelativistic atomic frequency shifts and lifetimes

Abstract

We present a quantum electrodynamic treatment of radiative corrections in atoms which is patterned after Lorentz's classical work on radiation damping. Expressions for both radiative lifetimes and frequency shifts are calculated through second order in the electric charge for a fictitious two-level model atom and for a spinless one-electron atom with an infinite number of arbitrarily spaced energy levels. In order to apply the classical ideas of Lorentz to quantum-electrodynamic problems of this kind we work directly with the relevant dynamical variables of the atom and field. The calculations are carried out entirely in the Heisenberg picture by recognizing the importance of radiation reaction. The quantized-field operator equations are integrated with the aid of a Markov approximation. The part of the integrated field that arises from the atomic electron current operator, the radiation-reaction field, is shown to be solely responsible for the atom's linewidths and frequency shifts. It is clear that it is unnecessary to invoke vacuum fluctuations at any stage. The usual quantum electrodynamic exponential decay law is found to govern the expectation values of the energy and dipole moment of the atom as well as the radiated-field amplitude. The theory nevertheless remains unitary. The Heisenberg operator commutation relations are shown to be valid at all times, and the Markov approximation is justified for times longer than a reciprocal transition frequency.