Furry picture

A full account of the theory of relativistic molecular structure based on standard QED in the Furry picture will be found in a number of publications such as [7, Chapter 22], [8, Chapter 3]. These accounts use a relativistic second quantized formalism. For present purposes, it is sufficient to present the structure of BERTHA in terms of the unquantized effective Dirac-Coulomb-Breit (DCB) A-electron Hamiltonian ... 

Feynman rules for the Green function. In the Furry picture, in addition to the standard Feynman rules in the energy representation (see [24,13]), the following vertices and lines appear (we assume that the Coulomb gauge is used)... 

From this presentation it is clear that any expansion in Za is useless even in the region of intermediate Z and the calculation has to be performed to all orders of Za. Methods for these calculations were developed by decomposing the intermediate bound state into several terms but keeping all orders of Za. In the following discussion we employ the usual bound interaction ( Furry ) picture of QED. The external field is considered as instantaneous Coulomb interaction according to an infinitely heavy atomic nucleus. Deviations from this assumption result only in minor corrections and will be discussed later on. The Furry picture results in a possible separation of time and space variables contrary to the covariant formulation of eqs. (6-8). 

Here we again employed the Furry picture. Introducing the vacuum polarization charge density... 

The effect of the nuclear mass was already mentioned in the introduction. In the Furry picture which is employed in the calculations of QED effects on bound electron states a static external field is assumed which corresponds to an infinitely heavy nucleus. In a non-relativistic approximation its finite mass is encountered by the reduced mass correction similar to the two-body problem in classical mechanics. In a relativistic treatment, however, this approach is oversimplyfied. Recently Artemyev et al. [42, 43] almost solved the whole problem by considering the nucleus as a simple Dirac particle with spin 1 /2, mass M and charge Ze. The interaction of the two Dirac particles electron and nucleus leads to a quasipotential equation in the center-of-mass system,... 

One should note, though, that with a well-chosen potential, for instance the field of bare nuclei, the Furry picture is likely a good approximation to the fuzzy picture. 

For the bound electrons (more exactly for the electrons moving in external fields) it is convenient to develop PT based on the bound electron wave functions. This representation is cadled Furry representation, or the Furry picture... 

Within the Furry picture a many-electron atom is considered as a system of electrons moving in the field of a nucleus and interacting with each other via the electromagnetic field. 

Note that in the Furry picture the IV-symbol in Eq(96) should be omitted. Otherwise terms that describe the current induced in the vacuum by the ex-... 

A detailed description of the Feynman graph techniques and the correspondence rules within the Furry picture for bound-state QED can be found in... 

In this way all contributions to and 7 resulting from the virtual creation of particle-antiparticle pairs in the Furry picture defined by the KS potential (63) are suppressed. 

In the case of the many-body terms the neglect of vacuum corrections is no longer uniquely defined. Two possible approaches can be distinguished, both set up within the KS Furry picture in order to be consistent with (70). In the no-pair approximation the contribution of the negative energy solutions to all intermediate sums over states are ignored. For instance, the DPT analog of the... 

This classic text features a careful presentation without lacking any details and explains aU foimdations of QED. It can also be warmly recommended for more advanced topics of QED, such as Feynman diagrams, the Furry picture etc. 

As a final remark we may comment on the fact that we need to study the two-electron problem in the attractive external potential of an atomic nucleus, hence, as a bound-state problem. It is immediately seen that this affects, for instance, the expansion in terms of zeroth-order state functions in Eq. (8.22), where bound states of the one-electron problem rather than free-particle states become the basis for the construction of the wave function (and wave-function operators in second quantization). The situation is, however, more delicate than one might think and reference is usually made to the discussion of this issue provided by Furry [216] (Furry picture). Of course, it is of fundamental importance to the QED basis of quantum chemistry. However, as a truly second-quantized QED approach, we abandon it in our semi-classical picture and refer to Schweber for more details [165, p. 566]. Instead, we may adopt from this section only the possibility to include either the Gaunt or the Breit operators in a first-quantized many-particle Hamiltonian. 

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