Quantum electrodynamics photon coupling

An analogous process in 0(3) quantum electrodynamics involves, following Crowell [17], the coupling of the electron with a nonlinear photon coupling corresponding to the energy shift ... 

The exact quantum theoretical treatment of the dispersion effect involves quantizing matter and electromagnetic fields as well. The coupled electron-photon system is to be treated on the basis of quantum electrodynamics. Using the method of second quantization, it is possible to build up the total Hamiltonian from an electron Hamiltonian H, a photon Hamiltonian and an electron-photon interaction operator Hin,. The dispersion energy between two particles now results in fourth order perturbation. Each contribution is due to the interaction of two electrons with, fwo photons. 

It is one of the objectives of the quantum electrodynamic procedure to check the errors and limits of these semiclassical approaches. In particular there is the question of statistics. What is the reason for the dominant influence of Bose statistics in the final energy expression Another question is up to which order of the electron-photon coupling operator do the semiclassical approaches hold Is one of these approaches more powerful than the other or limited to certain molecules or separations ... 

The quantum electrodynamic procedure replaces electrons and photons by quasi-particles. The quasi-electrons are renormalized with respect to terms quadratic in the electron-photon coupling operator. They differ from Fermi statistics with respect to fourth order terms. Similarly, the quasi-photons are renormalized with respect to terms quadratic in the electron-photon coupling operator. They differ from Bose statistics with respect to fourth order terms. 

The exact quantum electrodynamic treatment of the coupled electron-photon system is shown in the right-hand box of Fig. 2. 

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