Many-Electron QED with Redefined Vacuum Approach

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

Automated summary

The redefined vacuum approach is a powerful tool in deriving formulas within the bound-state QED perturbation theory, particularly for single particle excitation. By deducing many-electron contributions from simple one-electron QED diagrams, the method allows for straightforward derivation and identification of gauge-invariant subsets based on the gauge invariance of the diagrams.