dorsal/arxiv
View SchemaMany-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
| Authors | Ingvar Lindgren |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502141 |
| URL | https://arxiv.org/abs/quant-ph/0502141 |
| DOI | 10.1139/p05-027 |
Abstract
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.
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"abstract": "The connection between many-body theory (MBPT)--in perturbative and\nnon-perturbative form--and quantum-electrodynamics (QED) is reviewed for\nsystems of two fermions in an external field. The treatment is mainly based\nupon the recently developed covariant-evolution-operator method for QED\ncalculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a\nstructure quite akin to that of many-body perturbation theory. At the same time\nthis procedure is closely connected to the S-matrix and the Green\u0027s-function\nformalisms and can therefore serve as a bridge between various approaches. It\nis demonstrated that the MBPT-QED scheme, when carried to all orders, leads to\na Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A\nBloch equation in commutator form that can be used for an \"extended\" or\nquasi-degenerate model space is derived. It has the same relation to the BS\nequation as has the standard Bloch equation to the ordinary Schroedinger\nequation and can be used to generate a perturbation expansion compatible with\nthe BS equation also for a quasi-degenerate model space.",
"arxiv_id": "quant-ph/0502141",
"authors": [
"Ingvar Lindgren"
],
"categories": [
"quant-ph"
],
"doi": "10.1139/p05-027",
"title": "Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation",
"url": "https://arxiv.org/abs/quant-ph/0502141"
},
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