This work is a collection of initial calculations and formal considerations within the Salpeter–Sucher exact equal-time relativistic quantum electrodynamics framework. The calculations are carried out as preparation for the computation of pair, retardation, and radiative corrections to the relativistic energy of correlated two-spin-1/2-fermion systems. In this work, particular attention is paid to the retardation and the “one-loop” self-energy corrections, which are known to be among the largest corrections to the correlated relativistic energy. The theoretical development is supplemented with identifying formal connections to the non-relativistic quantum electrodynamics framework, which is based on a correlated but non-relativistic reference, as well as to the “1/Z approach,” which is built on a relativistic but independent-particle zeroth order. The two complementary directions currently provide the theoretical framework for light atomic–molecular precision spectroscopy and heavy-atom phenomena. The present theoretical efforts pave the way for relativistic QED corrections to (explicitly) correlated relativistic computations.
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