Bloch, F.; Nordsieck, A.; Note on the Radiation Field of the Electron
Phys. Rev. 52 (1937) 54;
Reprinted in The Physical Review - the First Hundred Years, AIP Press (1995) CD-ROM.
Selected Papers on Quantum Electrodynamics, editor J. Schwinger, Dover Publications, Inc., New York (1958) 129.
Previous methods of treating radiative corrections in nonstationary processes such as the scattering of an electron in an atomic field or the emission of a -ray, by an expansion in powers of e2/h c, are defective in that they predict infinite low frequency corrections to the transition probabilities. This difficulty can be avoided by a method developed here which is based on the alternative assumption that e2
/mc3, h /mc2 and h /c p (=angular frequency of radiation, p = change in momentum of electron) are small compared to unity. In contrast to the expansion in powers of e2/ h c, this permits the transition to the classical limit h = 0. External perturbations on the electron
are treated in the Born approximation. It is shown that for frequencies such that the above three parameters are negligible the quantum mechanical calculation yields just the directly reinterpreted results of the classical formulae, namely that the total probability of a given change in the motion of the electron is unaffected by the interaction with radiation, and that the mean number of emitted quanta is infinite in such a way that the mean radiated energy is equal to the energy radiated classically
in the corresponding trajectory.
Related references See also N. F. Mott, Proc. Camb. Phil. Soc. 27 (1931) 255;
A. Sommerfeld, Annalen der Physik. Leipzig 11 (1931) 257;
W. Pauli, Handbuch der Phys. 24/1 (1933) 266;
J. K. Knipp and G. E. Uhlenbeck, Physica 3 (1936) 425;
F. Bloch, Phys. Rev. 50 (1936) 272;
H. Bethe and W. Heitler, Proc. Roy. Soc. A146 (1934) 83;