Quantum electrodynamics. I. A covariant formulation. Offprint from: Physical Review, Vol. 74, No. 10, pp. 1439-1461, November 15, 1948

THE INVENTION OF RENORMALIZATION IN QUANTUM ELECTRODYNAMICS. First edition, extremely rare offprint, of Schwinger's invention of the theory of renormalization in quantum electrodynamics (QED). Schwinger (1918-94) shared the Nobel Prize in Physics 1965 with Richard Feynman and Sin-Itiro Tomonaga "for their fundamental work in quantum electrodynamics." "Renormalization was one of the great peaks of the development of fundamental physics in this century. Scaling the peak was a difficult enterprise. It required technical skill, courage, subtle judgements and great persistence. Many people had contributed to this enterprise. Many, many people can climb the peak now. But, the person who first conquered the peak was Julian Schwinger" (Nobel laureate C. N. Yang in Ng (ed.), p. 177). Feynman is justly celebrated for his formulation of QED in terms of 'Feynman diagrams', but his two papers on QED appeared almost a year after Schwinger's. "The formalism found by Tomonaga and his school was essentially identical to that developed by Schwinger five years later; yet they at the time calculated nothing, nor did they discover renormalization. That was certainly no reflection on the ability of the Japanese; Schwinger could not have carried the formalism to its logical conclusion without the impetus of the postwar experiments, which overcame prewar paralysis by showing that the quantum corrections `were neither infinite nor zero, but finite and small, and demanded understanding'" (Milton (ed.), p. 7). Quantum electrodynamics (QED) is the quantum theory of the interactions between electrically charged particles and the electromagnetic field (between electrons, positrons and photons, for example). It has been called "the jewel of physics" because of the extreme accuracy of its predictions: for example, the value of the magnetic moment of the electron calculated from QED agrees with the measured value to within a few parts in 100,000,000,000. QED was born in 1928, with Dirac's paper 'The quantum theory of the emission and absorption of radiation.' Although a major advance, this theory, and its development over the next decade by Heisenberg, Jordan, Pauli and others, encountered serious difficulties: it predicted an infinite self-energy for the electron, and several other such 'divergences'. Overcoming this problem took two decades, almost as long as it took from the first appearance of the quantum idea in 1900 to the creation of quantum mechanics by Heisenberg, Dirac, and Schrödinger in 1925/26. Once completed, QED became the model quantum field theory. Such theories now successfully describe not only the electromagnetic but also the weak and the strong interactions between particles. OCLC lists the University of Florida only (probably the copy of P. A. M. Dirac, who spent his final years there). No copies on RBH. Provenance: Abraham Pais (1918-2000), Dutch-American physicist and science historian (signature on front wrapper). Pais is known for his contributions to particle physics. In later years he became interested in documenting the history of modern physics, publishing a celebrated biography of Einstein (Subtle is the Lord, 1984). The problem of infinities "appeared even in classical electrodynamics. The electric field of a point charge contains an infinite amount of energy. Lorentz therefore attributed a finite extension, the classical electron radius, to the electron. Also, an accelerated charge seems to possess an abnormally high mass since energy was not only needed to overcome inertia but also to power the radiation it emits. This effect could be accounted for, if one assumed that the field of the charge acts back on the charge itself. Planck in 1900 and, in particular, Einstein in 1905 had described the electromagnetic field in a box as a set of quanta; but in non-relativistic quantum mechanics only massive particles, usually the electrons, were considered quanta, whereas the field was treated as classical. In 1927, Dirac introduced a m.…