Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation

The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and the Green's-function formalisms and can therefore serve as a bridge between various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. It has the same relation to the BS equation as has the standard Bloch equation to the ordinary Schroedinger equation and can be used to generate a perturbation expansion compatible with the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic

Combining Quantum Electrodynamics and Electron Correlation

There is presently a large interest in studying highly charged ions in order to investigate the effects of quantum-electrodynamics (QED) at very strong fields. Such experiments can be performed at large accelerators, like that at GSI in Darmstadt, where the big FAIR facility is under construction. Accurate experiments on light and medium-heavy ions can also be performed by means of laser and X-ray spectroscopy. To obtain valuable information, accurate theoretical results are required to compare with. The most accurate procedures presently used for calculations on simple atomic systems are (i) all-order many-body perturbative expansion with added first-order analytical QED energy corrections, and (ii) two-photon QED calculations. These methods have the shortcoming that the combination of QED and correlational effects (beyond lowest order) is completely missing. We have developed a third procedure, which can remedy this shortcoming. Here, the energy-dependent QED effects are included directly into the atomic wave function, which is possible with the procedure that we have recently developed. The calculations are performed using the Coulomb gauge, which is most appropriate for the combined effect. Since QED effects, like the Lamb shift, have never been calculated in that gauge, this has required some development. This is now being implemented in our computational procedure, and some numerical results are presented. © Springer International Publishing Switzerland 2015