Potential independence of the solution to the relativistic many-body problem and the role of negative-energy states in heliumlike ions

Abstract

Solving the relativistic many-body problem using either many-body perturbation theory or configuration-interaction techniques is shown to lead to energies that depend slightly on the starting potential if the effects of virtual electron-positron pairs are excluded. If they are included without a correct implementation of quantum electrodynamics (QED), while this dependence is eliminated in a mathematical sense, the procedure is shown to give unphysical answers. When instead the effects of virtual electron-positron pairs are included using the S-matrix theory implementation of QED, the potential dependence is shown to be eliminated in a physical way through the inclusion of a particular class of Feynman diagrams.