Second-order radiative and retardation corrections

Derive the second-order radiative and retardation corrections omitted from the second-order relativistic many-body perturbation-theory expansion of the QED Luttinger–Ward functional.

Background

The effective-action expansion identifies the ordinary second-order relativistic many-body perturbation-theory contribution and separates additional radiative, retardation, and pair effects. The paper evaluates selected first-order transverse Breit and second-order pair corrections, but does not compute the corresponding second-order radiative and retardation terms. These omitted contributions are explicitly reserved for future work.

References

In the following sections, we will compute the second order instantaneous contributions, and show that this pertubative treatment yields the known shifts from RMBPT in addition to radiative and retardation corrections that we will cover in future work.

— A QED Functional Formulation of Relativistic Many-Body Perturbation Theory in Atoms  (2610.22216 - Jonge et al., 15 Oct 2026) in Section ‘Expansion of the Effective Action around the no-pair DHFC Saddle’

Similarly to the previous section, one can obtain the retardation corrections at this point, which we once again defer to future dedicated work on this issue.

— A QED Functional Formulation of Relativistic Many-Body Perturbation Theory in Atoms  (2610.22216 - Jonge et al., 15 Oct 2026) in Section ‘Atoms with one valence electron’