On the choice of the electron-electron potential in relativistic atomic physics

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Abstract
In the calculation of relativistic effects in the structure of many-electron atoms there are two popular choices for the operator V used to represent the electron-electron interaction. One of these, VI, is associated with the use of the Coulomb gauge propagator for photons whereas the other, VII, is associated with the use of the Feynman gauge propagator. However, in contrast to VI, the non-perturbative use of VII leads to energy levels which are already incorrect in order alpha 4m. This fact provides a quantitative argument for preferring VI to VII.