Gauges Feynman

In (2.47) we have again chosen to work in Feynman gauge, which is technically simplest to handle. This choice does not introduce any gauge dependence, as demonstrated in [19]. Thus E is a well-defined functional of the (ti -P and e -. The corresponding exchange potential can be evaluated using the ROPM in the order (see Sections). 

The total contribution of all nineteen diagrams to HFS was first calculated purely numerically in the Feynman gauge in the NRQED framework in [22, 23]. The semianalytic skeleton integral calculation in the Yennie gauge was completed a bit later in [26, 27]... 

Nonlogarithmic radiative-recoil corrections to HFS were first calculated numerically in the Yennie gauge [35, 25] and then analytically in the Feynman gauge [31]... 

Here for c 1 we have the Feynman gauge, and , = 0 is the Landau gauge. This gauge fixing term will enter into the massive boson propagators for the A 3 field. The propagator will be of the form... 

I. Lindgren, H. Persson, Sten Salomonson, L. Labzowsky, Full QED calculations of two-photon exchange for heliumlike systems Analysis in the Coulomb and Feynman gauges, Phys. Rev. A 51 (2) (1995) 1167. 

The diagram SESE a), that is called also loop-after-loop , consists of irreducible and reducible parts (see Fig. 3). We consider first of all the irreducible contribution, which can be renormalized and evaluated separately since it does not contain infrared divergencies in the Feynman gauge. The renormalized expression for this contribution can be written as... 

This Green function is analytic in the complex energy plane except for the bound-state poles at En, with branch points at = 1 and cuts along the real axis for E > 1. Bound states occur only at energies E > 0. The firee-photon propagator appears as a time-ordered product of firee-photon field operators (in Feynman gauge)... 

On the other hand, there is also no fundamental problem with restricting RDFT to the Coulomb or Coulomb-Breit level. Choosing the Feynman gauge as used for the Hamiltonian (4.1), the full D is explicitly given by... 

We now turn to the second part of Eq. (1), i.e. the bound-state mass counter term. This term is defined as the free-electron self energy, in Feynman gauge, calculated for a momentum distribution determined by the bound state (French and Weisskopf [17]) and can be expressed in the following symmetric partial-wave form which is analogous to Eq. (9)... 

Two different procedures were used for the removal of the reference state singularities and the derivation of RSC. As it was shown in [12], the Coulomb-Coulomb contribution to RSC is absent. The RSC were first introduced in QED in [13] in the frames of the Green function formalism in the Feynman gauge [13,14]. The expressions for RSC are much simplified in the equal energies case (Ea = Eb), i.e. for the ground state of the two-electron ion. The explicit expression for the equal energies correction was derived in [15]... 

In the Feynman gauge the equal-energy RSC expressions have been obtained in [21] by the modified Green functions approach [22] and in [9,10] in the framework of S-matrix adiabatic approach. The unequal energies (Ea / Eg) Coulomb-Breit RSC (box) were derived in [20] by the line profile approach and RSC (cross) were derived for this case by the same method in [23]. 

The unequal-energies RSC in the Feynman gauge have been derived by the modified Green function approach in [24]. 

The numerical calculations for the ground state (equal energies case) of the He-like heavy ions were given in [9,10]. The Feynman gauge calculations include also the Breit-Breit contributions. Since for these contributions the Eq. (1.3) does not hold, the total RSC was nonzero. 

Using Feynman gauge for the photon propagator one finds that the lowest-order contribution to M, regarded as a power series in eje2, is given by... 

On using Feynman gauge to write down the one-photon exchange amplitude, one gets... 

The expression for the photon propagator in the Feynman gauge looks like ... 

Numerical calculations of the SE with the use of the direct potential expansion were performed in [66] using the Feynman gauge for 2=70,80,90. A part of the higher-order SE correction was also evaluated for high Z with this method... 

---