Many-Electron QED with Redefined Vacuum Approach

Abstract

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.

Symbolic Evaluation of Expressions from Racah’s Algebra

“…While, perhaps, such a graphical approach appears to be more elegant to the reader, it becomes tedious and prone to errors if the correct phase and weight factors need to be determined for complex diagrams. Similar tasks will occur in the future if the two-photon (QED) exchange diagrams are to be evaluated for open-shell atoms [47].…”

QED approach to valence-hole excitation in closed shell systems

“…Thus, several additional gauge-invariant subsets were identified. Later, we applied it to more sophisticated electron structures generalizing to either N valence electrons or N holes cases [37]. As an * Electronic address: romain.soguel@uni-jena.de example, we presented the complete set of formal expressions for BSQED corrections up to the second-order in α for the single-hole picture [37].…”

“…Later, we applied it to more sophisticated electron structures generalizing to either N valence electrons or N holes cases [37]. As an * Electronic address: romain.soguel@uni-jena.de example, we presented the complete set of formal expressions for BSQED corrections up to the second-order in α for the single-hole picture [37]. Thus, the situation when both valence electrons and holes are involved in the description of a state has not been considered so far within the vacuum redefinition method.…”

Some Current Trends in Atomic Theory

“…The present level of accuracy required accounts for quantum electrodynamics (QED) effects not only for the simplest one-, or two-electron atoms, but also for many-electron atoms and molecules. Three papers of this Special Issue are devoted to the QED calculations of the bound many-electron systems [1][2][3]. Yerokhin et al [1] describe high order QED calculation of He with the help of the two-electron exponential basis functions.…”

“…Soguel et al [2] use the redefined vacuum approach for the bound-state QED perturbation theory of many-electron systems. This approach drastically reduces the complexity of the many-electron QED expressions keeping only valence electrons, or vacancies under consideration.…”