Use of the classical approximation in quantum electrodynamics

Approximations commonly used in the study of the classical limit of quantum mechanics are applied, with justification, to quantum electrodynamics. First, the infrared divergence in the scattering of two charged particles is examined with the help of a remarkable series of Feynman diagrams, which in particular preserves gauge invariance and a correct static limit. Looking for the poles in energy of the scattering amplitude, a formula for the binding energies of two charged particles, which generalizes the Balmer formula and takes into account the correct relativistic kinematics, has been derived. A second type of applications concerns phenomena due to the interaction of the electromagnetic field with the vacuum current and charge fluctuations. For instance, when the intensities become very high, the theory predicts the creation of electron-positron pairs by the field. The creation rate is known in the limit of static fields, and the aim of these calculations was to demonstrate the role of frequency in the domain starting from the lowest frequencies up to X-rays. The pair production rate was found to be entirely negligible, even for the most intense laser beams. An increase in frequency, even up to several tens of keV, did not have any effect on the pair production. (author)