Combination of many-body perturbation theory and quantum electrodynamics

A procedure for energy-dependent perturbation expansion has been developed, based upon the covariant evolution operator method. This makes it possible to treat energy-dependent perturbations very much like the energy-independent ones in standard many-body perturbation theory. This has been applied to the non-radiative QED perturbations (retardation and virtual electron-positron pairs) as well as the radiative ones (electron self-energy, vacuum polarization and vertex correction). The combination of QED and electron correlation, beyond two-photon exchange, has been evaluated, using the Coulomb gauge. It turned out that in that gauge the extremely time-consuming model-space contributions of the self-energy and vertex corrections do not have to be evaluated in full. In the Feynman gauge no sensible results could be obtained in this way, as is demonstrated by the numerical results.