The radiation theories of Tomonaga, Schwinger, and Feynman, pp. 486-504 in Physical Review Vol. 75, No. 3, February 1, 1949 [With:] The S Matrix in Quantum Electrodynamics, pp. 1736-55 in Physical Review Vol. 75, No. 11, June 1, 1949. THE EQUIVALENCE OF THE FEYNMAN, SCHWINGER & TOMONAGA FORMULATIONS OF QED

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First edition, journal issues in original printed wrappers, of Dyson's proof of the equivalence between Richard Feynman's diagram-based approach to quantum electrodynamics (QED) and Julius Schwinger and Sin-Itiro Tomonaga's operator method approach. Dyson, "one of England's two or three most brilliant mathematical prodigies" (Gleick, Genius, p. 235), was then a graduate student at Cornell, where Feynman was teaching. "A detailed comparison between the different approaches to QED proposed by Feynman, by Tomonaga, and by Schwinger was given by Freeman Dyson, He stressed that 'the advantages of the Feynman theory are simplicity and ease of application, while those of Tomonaga-Schwinger are generality and theoretical completeness.' At that time, when much of Feynman's theory was still unpublished, Dyson (who knew about Feynman's work from personal discussions with him) undertook to investigate the relations between these three approaches, which at first seemed to be completely different from each other, and to establish their equivalence" (Mehra, Beat of a Different Drum, p. 314). "Dyson realized that Feynman and Schwinger were both dealing with different versions of Heisenberg's S-matrix [which encodes the probabilities associated with the different routes from the different possible initial states to the different possible final states]. He then formally introduced 'time-ordering' and provided a unified approach by demonstrating the equivalence of the Feynman and Schwinger-Tomonaga theories. This approach also allowed him to show how the Schwinger theory could be greatly simplified and extended to all orders of the perturbation expansion. Dyson's time-ordering idea was actually obtained from discussions with Feynman, who later explored and fully developed it into his time-ordered operator calculus" (Gill, The Feynman-Dyson view, J. Phys.: Conf. Ser. 845, 2017). "A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a point further than that reached by these authors, in the discussion of higher order radiative reactions and vacuum polarization phenomena. However, the theory of these higher order processes is a program rather than a definitive theory, since no general proof of the convergence of these effects is attempted. The chief results obtained are (a) a demonstration of the equivalence of the Feynman and Schwinger theories, and (b) a considerable simplification of the procedure involved in applying the Schwinger theory to particular problems, the simplification being the greater the more complicated the problem" (Abstract). At an American Physical Society meeting just after the end of the War, "Dyson found himself almost as much a hero as Schwinger had been the year before. Sitting in the audience with Feynman beside him, he listened as a speaker talked admiringly of 'the beautiful theory of Feynman-Dyson'. Feynman said loudly, 'Well, Doc, you're in'" (Gleick, p. 270). Two complete journal issues, large 8vo, pp. 351-535; 1637-1780. Original printed wrappers (spine of February issue darkened and with minor loss at ends). N° de ref. del artículo ABE-1639650343261

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