A QED Functional Formulation of Relativistic Many-Body Perturbation Theory in Atoms

Abstract: We systematically derive relativistic many-body perturbation theory (RMBPT) from the two-particle irreducible effective action of quantum electrodynamics (QED) in the Furry picture, giving an organisational and diagrammatic framework for both correlation and radiative corrections in many-electron atoms. We further discuss that RMBPT is a well-defined subset of QED effects evaluated on a redefined vacuum, such that the interplay between correlation and radiative effects becomes transparent. We use this to derive QED corrections to the interelectronic interaction of atomic systems, yielding the transverse (frequency-dependent Breit) photon-exchange corrections, including retardation. Of those corrections, we numerically evaluate the first-order transverse photon-exchange corrections, which complement the conventional RMBPT based on the Dirac-Coulomb no-pair Hamiltonian.