Quantum electrodynamics photon exchange

Strictly speaking the description of such local measurements can be carried out only within the framework of quantum electrodynamics, i.e, in a theory wherein photons can be exchanged between the measuring apparatus and the current distribution being measured. 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

The energy operator considered above is an approximation, in which only the lowest terms of the correction for the retardation of the interaction are taken into account. More general is the formal quantum-electrodynamical interaction energy operator in the approximation of the exchange of one virtual photon [58]... 

In previous chapters we considered elementary crystal excitation taking into account only the Coulomb interaction between carriers. From the point of view of quantum electrodynamics (see, for example, (1)) such an interaction is conditioned by an exchange of virtual scalar and longitudinal photons, so that the potential energy, corresponding to this interaction, depends on the carrier positions and not on their velocity distribution. As is well-known, the exchange of virtual transverse photons leads to the so-called retarded interaction between charges. 

According to quantum electrodynamics, the electromagnetic interaction is mediated by photons. For instance, one of the electric charges emits a photon, and the other one absorbs it. Yukawa (1935) supposed that the interaction between nucleons is also mediated by the exchange of field quanta, and the predicted rest energy of the field quantum (called meson) is 140 MeV. After the discovery of n mesons (Lattes et al. 1947) the quanta of the meson field have been identified with n mesons, which have approximately the same rest energy. 

The procedures for many-body perturbation calculations (MBPT) for atomic and molecular systems are nowadays very well developed, and the dominating electrostatic as well as magnetic perturbations can be taken to essentially all orders of perturbation theory (see, for instance, [1]). Less pronounced, but in many cases still quite significant, are the quantum electrodynamical (QED) perturbations—retardation, virtual pairs, electron self-energy, vacuum polarization and vertex correction. Sophisticated procedures for their evaluation have also been developed, but for practical reasons such calculations are prohibitive beyond second order (two-photon exchange). Pure QED effects beyond that level can be expected to be very small, but the combination of QED and electrostatic perturbations (electron correlation) can be significant. However, none of the previously existing methods for MBPT or QED calculations is suited for this type of calculation. 

Fig. 6.11 A quantum computer proposal in the context of optical cavity quantum electrodynamics. Atoms or ions are used to represent the qubits and are trapped within two mirrors so as to communicate with each other by photon exchange. The qubits have to be addressed individually by laser beams.

---