多体QED微扰理论：与Bethe-Salpeter方程的联系
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
摘要：
多体理论（MBPT）-在微扰和非微扰形式-和量子电动力学（QED）之间的联系进行审查的两个费米子在外场系统。处理主要是基于最近开发的协变演化算子方法的QED计算[Lindgren et al. Phys. Rep. 389，161（2004）]，其结构非常类似于多体微扰理论。与此同时，这一过程与S-矩阵和格林函数形式主义密切相关，因此可以作为各种方法之间的桥梁。结果表明，MBPT-QED方案，当进行到所有的订单，导致薛定谔方程，等价于Bethe-Salpeter（BS）方程。导出了一个可用于“扩展”或准退化模型空间的换位子形式的布洛赫方程。它与BS方程的关系与标准Bloch方程与普通Schroedinger方程的关系相同，并且可以用于产生与BS方程相容的微扰展开，也适用于准简并模型空间。
英文摘要：
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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