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

The connection between many-body theory (MBPT)—in perturbative and nonperturbative 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’sfunction 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 Schrödinger-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 Schrödinger equation and can be used to generate a perturbation expansion compatible with the BS equation also for a quasi-degenerate model space. PACS Nos.: 31.10+z, 31.15Md, 31.30Jv Résumé : French version of abstract (supplied by CJP) [Traduit par la rédaction] Submitted 25 Jan. 2005, Corrected 8 Feb. 2005