Lectures on quantum electrodynamics

This work is based on graduate course that the author gave at Rangoon (Yangon) University between 1994 and 2006 . Dirac realised while going through his unpublished notes in May 1963 (M Jammer 1966 "The Conceptual Development of Quantum Mechanics" New York:McGraw-Hill) that some of the ideas he rejected previously could now be instrumental in resolving the divergence difficulties in QED. In his 1963/64 lectures on quantum field theory given at Yeshiva University he was able to present a novel derivation of the Schwinger term and of the Lamb shift using the Hamiltonian formalism that he had developed in 1950's (Dirac 1950 Can J Math vol 2, 129;1951 Can J Math vol 3,1). This field theoretical approach had earlier helped Dirac and other physicists to discuss the problem of quantization of the gravitational field besides bringing it closer to the other branches of physics (B S DeWitt 1967 Phys Rev vol 160, 113). We have chosen the field theoretical approach à la Dirac since it is nearest to the approach adopted by French and Weisskopf who were the first to work on the Lamb shift problem of the hydrogen atom and who obtained the first correct result for the Lamb shift. French and Weisskopf (1949 Phys Rev vol 75, 1240) were using Dirac's hole theory for fermions which could be easily generalized to quantum theory of fields in terms of creation and annihilation operators. For sometime Feynman and Schwinger did not deem it necessary to use such operators in their calculations. As a direct consequence these two brilliant physicists made the joining mistake and the mistake with the Uehling term (vacuum polarization) leading to incorrect results in their initial computation of the Lamb shift. Since the incorrect results of Feynman and Schwinger did not agree with their (correct!) result, French and Weisskopf did not dare to publish their results earlier (S S Schweber 1994 "QED and the Men who made It" Princeton:PUP). Bethe,Feynman,Schwinger and many American physicists were successfully doing physics without recourse to formal quantum field theory. Feynman and Schwinger did not get " their numbers right" in their Lamb shift work at first but their confidence in themselves eventually won them a share in the 1965 Nobel prize for physics. In reality it was French and Weisskopf who first obtained the correct result followed by Kroll and Lamb . Both of the two papers by these authors , however , were not included in the collected papers on QED edited by Schwinger in 1958 (“ Quantum Electrodynamics” New York: Dover).
Dyson wrote in 1993 (Physics World August p33) that"it is remarkable among the "wonderful papers " in the volume 73 of 1948 Phys Rev , the paper by Dirac is the only one concerned with quantum field theory. Dirac was the voice from another world ". Even in 1933 that Dirac had a more complete understanding of the situation than his contemporaries can be seen from his letter to Niels Bohr (Pais A 1990 in "Reminisences of a Great Physicist" Ed Kursunoglu & Wigner Cambridge:CUP) "Peierls and I have been looking into the question of the change in the distribution of negative energy electrons ( meaning vacuum) produced by a static electric field. We find that this changed distribution causes a partial neutralization of the charge (charge renormalization) producing the field. If we neglect the distribution that the field produces in negative energy electrons (vacuum polarization) with energies less than -137mc^2 ( -137x electron rest mass energy), the neutralization of the charge (charge renormalization) produced by other negative energy electrons is small and is of the order of 136/137. The effective charges (physical charges) are what one measures in all the low energy experiments and the experimentally determined value of e must be the effective charge (physical charge) on an electron, the real value (bare charge) being slightly bigger [e+delta(e)] ". In October 1933 he also provided the general expression for the finite contribution to the vacuum polarization which was evaluated for an electron moving in a hydrogen-like atom by Uehling in 1935. Recall, if you will, that the troublesome vacuum polarization term created problems for both Schwinger and Feynman -initially (S S Schweber 1994 "QED and the Men who made It" Princeton:PUP).