Quantum electrodynamics of many-electron atoms

Abstract

The question of the validity of many body perturbation theory (MBPT) calculations that start from the Dirac-Coulomb Hamiltonian is addressed. An extension of the Furry representation of Quantum Electrodynamics (QED) is introduced in which the nuclear Coulomb field is replaced by a potential more relevant to many-electron atoms. QED perturbation theory for energies and matrix elements is set up and evaluated for exchanges of up to two photons. It is shown that in lowest and first order the expressions used in MBPT starting from the Dirac-Coulomb Hamiltonian are reproduced along with additional Lamb shift and Breit interaction contributions. In second order use of QED gives rise to slight differences with MBPT: however, simple rules pertaining to sums over negative energy states are given that eliminate possible difficulties corresponding to continuum dissolution.