Divergence 0 electrodynamics, quantum

Concluding Remarks.—We have come to the end of our exposition of some aspects of quantum electrodynamics. We have not delved in some of the more technical and difficult facets of the subject matter. Mention should, however, be made of what some of the difficulties are. Foremost at the technical level is perhaps the role played by the infrared divergences. The fact that the photon has zero mass not only gives rise to divergences in various matrix elements,20 but also implies... 

The ultraviolet divergence is generated by the diagrams with insertions of two anomalous magnetic moments in the heavy particle line. This should be expected since quantum electrodynamics of elementary particles with nonvanishing anomalous magnetic moments is nonrenormalizable. 

In U(l) quantum electrodynamics, the ultraviolet divergence is removed [17] by countering it with a similar term. For the free electron, there is the infinite term... 

Therefore quantum fluctuations in B<3) are accompanied by fluctuations in the transverse electric field. The ultraviolet divergence is probably unimportant [17] because of the co 2 dependence of the fluctuation. The infrared divergence is also damped statistically. The divergences in U(l) electrodynamics [6] can exist as a subset of 0(3) electrodynamics and can be absorbed into integrals that involve photon loop processes associated with quantum fluctuations in B(3 ... 

In Quantum Electrodynamics, renormalization was developed around 1950, especially by Schwinger, Feynman, and Dyson, in order to eliminate nonphysical ultraviolet divergences. 

This statement implies that not only the Coulomb interaction is included in Er and Exc but also the (retarded) Breit interaction. It thus points at the fact that a consistent and complete discussion of many-electron systems and consequently of RDFT must start from quantum electrodynamics (QED). RDFT necessruily has to reflect the various features of QED, both on the formal level and in the derivation of explicit functionals. The most important differences to the noiu-elativistic situation arise from the presence of infinite zero point energies and ultraviolet divergencies. In addition, finite vacuum corrections (vacuum polarization, Casimir energy) show up in both fundamental quantities of RDFT, the four current and the total energy. These issues have to be dealt with by a suitable renormalization procedure which ultimately relies on the renormalization of the vacuum Greens functions of QED. The first attempt to take... 

In polymer theory, infrared divergences are discussed as well the behaviour of the partition functions is analyzed at d < 4 and z oo. In other words, the dimension d proves to be marginal in polymer theory as well as in quantum electrodynamics and Landau-Ginzburg-Wilson s field theory. In particular, this explicitly manifests itself in the definition of z (see Kquation 9). 

This discussion has been included to show that our understanding of such an apparently simple phenomenon as spontaneous emission is not perhaps as complete as we would wish. Other difficulties which are connected with divergent expressions which occur in quantum electrodynamics are discussed by Leighton (1959, Ch. 20.12). 

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