Quantum electrodynamics. I. A covariant formulation. Offprint from: Physical Review, Vol. 74, No. 10, pp. 1439-1461, November 15, 1948.
[Lancaster and New York: American Physical Society, 1948]. 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 method he called second quantization, which allowed to describe the creation and annihilation, i.e., the emission and absorption of light quanta. With the advent of the positron also the creation and annihilation of electron–positron pairs had to be explained. Now new difficulties were encountered and eventually resolved by renormalization, the distinction between the ‘bare’ charge of the electron and that observed in experiment and, likewise, the distinction between its ‘bare’ and its observed mass. In a few words this highly technical mathematical procedure is usually explained as follows. In the strong field near a solitary electron ‘virtual’ electron–positron pairs exist. There is not enough energy for them to be ‘real’, i.e., to be detected as free particles, but, because of the uncertainty relation, they can exist for a short time before they annihilate again. They change the charge distribution near the electron (the effect is called vacuum polarization) and hence the observed charge” (Brandt). “It took new experimental data to catalyze this development. That data was presented at the famous Shelter Island meeting held in June 1947, a week before Schwinger’s wedding. There he, Feynman, Victor Weisskopf, Hans Bethe, and the other participants learned the details of the new experiments of Lamb and Retherford that confirmed the pre-war Pasternack effect, showing a splitting between the 2S1/2 and 2P1/2 states of hydrogen, that should be degenerate [have the same energy] according to Dirac's theory. In fact, on the way to the conference, Weisskopf and Schwinger speculated that quantum electrodynamics could explain this effect, and outlined the idea to Bethe there, who worked out the details, non-relativistically, on his famous train ride to Schenectady after the meeting. But the other experiment announced there was unexpected: This was the experiment by Rabi’s group and others of the hyperfine anomaly that would prove to mark the existence of an anomalous magnetic moment of the electron, differing from the value g = 2 again predicted by Dirac. Schwinger immediately saw this as the crucial calculation to carry out first, because it was purely relativistic, and much cleaner to understand theoretically, not involving the complication of bound states. However, he was delayed three months in beginning the calculation because of an extended honeymoon through the West. He did return to it in October, and by December 1947 had obtained the result g/2 = 1 + α/2π [where α ~ 1/137 is the fine-structure constant], completely consistent with experiment [‘On quantum-electrodynamics and the magnetic moment of the electron’]. He also saw how to compute the relativistic Lamb shift (although he did not have the details quite right) … In effect, he had solved all the fundamental problems that had plagued quantum electrodynamics in the 1930s: The infinities were entirely isolated in quantities that renormalized the mass and charge of the electron. Further progress, by himself and others, was thus a matter of technique. “During the next two years Schwinger developed two new approaches to quantum electrodynamics. His original approach, which made use of successive canonical transformations to isolate the infinities, while sufficient for calculating the anomalous magnetic moment of the electron, was noncovariant, and as such, led to inconsistent results. In particular, the magnetic moment appeared also as part of the Lamb shift calculation, through the coupling with the electric field implied by relativistic covariance; but the noncovariant scheme gave the wrong coefficient … So first at the Pocono Conference in April 1948, then in the Michigan Summer School that year, and finally in a series of three monumental papers, ‘Quantum Electrodynamics I, II, and III’, Schwinger set forth his covariant approach to QED. At about the same time Feynman was formulating his covariant path-integral approach; and although Feynman’s presentation at Pocono was not well-received, Feynman and Schwinger compared notes and realized that they had climbed the same mountain by different routes. Feynman’s systematic papers were published only after Dyson had proved the equivalence of Schwinger’s and Feynman’s schemes. “It is worth remarking that Schwinger’s approach was conservative. He took field theory at face value, and followed the conventional path of Pauli, Heisenberg, and Dirac. His genius was to recognize that the well-known divergences of the theory, which had stymied all pre-war progress, could be consistently isolated in renormalization of charge and mass. This bore a superficial resemblance to the ideas of Kramers advocated as early as 1938, but Kramers proceeded classically. He had insisted that first the classical theory had to be rendered finite and then quantized. That idea was a blind alley. Renormalization of quantum field theory is unquestionably the discovery of Schwinger [our emphasis]. Feynman was more interested in finding an alternative to field theory, eliminating entirely the photon field in favor of action at a distance. He was, by 1950, quite disappointed to realize that his approach was entirely equivalent to the conventional electrodynamics, in which electron and photon fields are treated on the same footing. “As early as January 1948, when Schwinger was expounding his noncovariant QED to overflow crowds at the American Physical Society meeting at Columbia University, he learned from Oppenheimer of the existence of the work of Tomonaga carried out in Tokyo during the terrible conditions of wartime. Tomonaga had independently invented the ‘Interaction Representation’ which Schwinger had used in his unpublished 1934 paper, and had come up with a covariant version of the Schrödinger equation as had Schwinger, which upon its Western rediscovery was dubbed by Oppenheimer the Tomonaga-Schwinger equation … 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” (Milton (ed.), pp. 5-7). ‘Quantum electrodynamics I’ is concerned with setting out the foundations of Schwinger’s covariant formulation of QED. We quote from its extended abstract: ‘Attempts to avoid the divergence difficulties of quantum electrodynamics by mutilation of the theory have been uniformly unsuccessful. The lack of convergence does indicate that a revision of electrodynamic concepts at ultrarelativistic energies is indeed necessary, but no appreciable alteration of the theory for moderate relativistic energies can be tolerated. The elementary phenomena in which divergences occur, in consequence of virtual transitions involving particles with unlimited energy, are the polarization of the vacuum and the self-energy of the electron, effects which essentially express the interaction of the electromagnetic and matter fields with their own vacuum fluctuations. The basic result of these fluctuation interactions is to alter the constants characterizing the properties of the individual fields, and their mutual coupling, albeit by infinite factors. The question is naturally posed whether all divergences can be isolated in such unobservable renormalization factors; more specifically, we inquire whether quantum electrodynamics can account unambiguously for the recently observed deviations from the Dirac electron theory, without the introduction of fundamentally new concepts. This paper, the first is a series devoted to the above question, is occupied with the formulation of a completely covariant electrodynamics. Manifest covariance with respect to Lorentz and gauge transformations is essential in a divergent theory since the use of a particular reference system or gauge in the course of calculation can result in a loss of covariance in view of the ambiguities that may be the concomitant of infinities.” “Schwinger was a child prodigy, publishing his first physics paper at age 16. He earned a bachelor’s degree (1937) and a doctorate (1939) from Columbia University in New York City, before engaging in postdoctoral studies at the University of California at Berkeley with physicist J. Robert Oppenheimer. Schwinger left Berkeley in the summer of 1941 to accept an instructorship at Purdue University, and in 1943 he joined the Radiation Laboratory at the Massachusetts Institute of Technology, where many scientists had been assembled to help with wartime research on radar. In the fall of 1945 Schwinger accepted an appointment at Harvard University and in 1947 became one of the youngest full professors in the school’s history. From 1972 until his death, Schwinger was a professor in the physics department at the University of California at Los Angeles” (Britannica). “In the post-quantum-mechanics era, few physicists, if any, have matched Julian Schwinger in contributions to and influence on the development of physics. A towering giant in theoretical physics, Schwinger left his indelible mark on such diverse fields as quantum mechanics, quantum field theory, electrodynamics, nuclear physics, statistical mechanics, atomic physics, elementary particle physics, gravity, and mathematical physics. On July 16, 1994, he succumbed to pancreatic cancer at the age of seventy-six” (Ng (ed.), p. vii). Brandt, The Harvest of a Century, 2009. Milton (ed.), Quantum Legacy. Seminal Papers of Julian Schwinger, 2000. Ng (ed.), Julian Schwinger. The Physicist, the Teacher, and the Man, 1996.
Large 8vo (267 x 201 mm), pp. 1439-1461, [1, blank]. Original printed self-wrappers.
Item #6186
Price: $9,500.00
