## Quantum Electrodynamics and Meson Theories. Notes on the Lectures by Professor Richard P. Feynman, Cornell University. Given at the California Institute of Technology, Pasadena, California, February 6 to March 2, 1950. Prepared by Carl W. Helstrom and Malvin A. Ruderman.

[Not published: California Institute of Technology, Pasadena, CA: 1950].

First and only edition, extremely rare, of the mimeographed notes of Feynman’s lecture course on meson theory, delivered as a visiting lecturer at Caltech (to which he moved permanently in the following year). Feynman had developed his distinctive diagrammatic approach while attempting to solve the problem of divergences in quantum electrodynamics (QED), the quantum theory of the interactions between electrically charged particles and the electromagnetic field (between electrons and photons, for example). “What captured most theorists’ attention soon after the war was not electron physics, but rather the embarrassment of riches suddenly pouring forth from the new accelerators. A flood of new particles, similar to but in many ways distinct from the familiar electrons and photons, surprised physicists when they began to probe high-energy interactions with the aid of accelerators, rather than relying only upon cosmic rays. As quickly became clear, the new particles – dubbed ‘mesotrons’ or ‘mesons’, since the masses of many of them were intermediate between electrons and protons – interacted with each other differently than electrons and photons did” (Kaiser, p. 57). Feynman became interested in meson theory while he was still perfecting his understanding of QED, but his ideas in this area remain unpublished (see below) – these notes are thus a key historical record of Feynman’s work on meson theory. Appearing 13 years before his famous three-volume *Lectures on Physics*, these particular notes were never published again, either separately or as part of his *Selected Papers*. They were probably produced in very small numbers for the graduate students and fellow faculty members who attended this advanced course. Widely regarded as the most brilliant, influential, and iconoclastic figure in theoretical physics in the post-World War II era, Feynman shared the Nobel Prize in Physics 1965 with Sin-Itiro Tomonaga and Julian Schwinger “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles.” “Mark Kac, the eminent Polish-American mathematician, wrote: ‘In science, as well as in other fields of human endeavor, there are two kinds of geniuses: the ‘ordinary’ and the ‘magicians’. An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with magicians … the working of their minds is for all intents and purposes incomprehensible … Richard Feynman [was] a magician of the highest caliber’” (*Biographical Memoirs of Fellows of the Royal Society of London* 48 (2002), p. 99). Not on OCLC. We are not aware of any other copy having appeared in commerce.

*Provenance*: Kenneth Hedberg (signature on title). Hedberg (1920-2019) graduated from Oregon State College (BS, 1943) and the California Institute of Technology (Ph. D., 1948), having studied chemistry at both institutions. While at Caltech, Hedberg studied under Verner Schomaker and interacted frequently with Linus Pauling. In 1956 Hedberg returned to Oregon State College where he joined the faculty of the chemistry department. Hedberg was elected a fellow of the American Physical Society and the American Association for the Advancement of Science. He was also elected to membership of the Norwegian Academy of Science and Letters.

At the end of the 1940s, physics was undergoing an extraordinary period of turmoil. “Newly discovered elementary particles, mesons and the like, were proliferating madly in the newly built particle accelerators. The elementary particle physics zoo was becoming embarrassingly crowded, so crowded in fact that it wasn’t clear which of the new blips on chart recorders and new tracks in bubble chambers might really represent new elementary particles and which were simply rearrangements of existing ones” (Krauss, p. 169). The most important of these new particles were the mesons, and it was actually in the study of a problem in meson theory that Feynman became convinced that his own methods were correct and represented a real advance.

The story is related by Schweber (pp. 454-6). At the January 1949 meeting of the American Physical Society in New York, Murray Slotnick, a student of Heitler and Bethe, gave a talk in which he described his calculation, in a so-called pseudoscalar meson theory, of the interaction between a neutron and the electrostatic field of an electron. Oppenheimer, who was in the audience, claimed that Slotnick’s results must be wrong, as they contradicted a theorem of Case, a postdoc at the Institute for Advanced Study. “When Feynman arrived in New York that evening, he was told what had happened at the session. He received a report on the calculations of Slotnick, the ‘numbers’ he had obtained after long and laborious computations and Oppenheimer’s slashing criticism. He was then asked to comment on the validity of Slotnick’s results in the light of ‘Case’s theorem’. Feynman had not heard of this theorem. In fact, up to that point he had not interested himself in meson-theoretic calculations at all. However, between the results of a person who had calculated ‘numbers’ and those of a formalist, the choice was clear. To corroborate his hunch that Slotnick was right, he got someone to explain to him what was meant by pure charged and symmetric meson theory, by pseudoscalar and pseudovector coupling, and he readily translated this information into the rules to compute the relevant matrix elements using his methods. He spent a few hours that evening calculating the difference between the proton and neutron electric form factor in various meson theories with both pseudoscalar and pseudovector couplings. The next morning he got a hold of Slotnick in order to compare his results with those that Slotnick had obtained, ‘because he wasn’t quite sure that he had transcribed properly the usual formulation of meson theories into his rules.’ When they compared their calculations, Slotnick had asked him the meaning of the *q*^{2} in Feynman’s formulas. Feynman answered that it was the momentum transferred by the electron in the scattering. Feynman had calculated the full vertex function for arbitrary momentum transfer. ‘Oh,’ said Slotnick, ‘my results are only for *q*^{2} = 0.’ ‘That’s OK,’ Feynman indicated, ‘I can readily take the *q*^{2} = 0 limit,’ which he proceeded to do and then compared his answer with Slotnick’s. They agreed. Slotnick was flabbergasted. He had spent close to two years on the problem and over six months on a calculation that took Feynman one evening … Feynman was excited:

‘This is when I really knew I had something. I didn’t really know I had something so wonderful as when this happened … That was the moment that I really knew I had to publish – that I had gotten ahead of the world … That was the moment when I got my Nobel Prize when Slotnick told me that he had been working two years. When I got the real prize it was really nothing, because I already knew I was a success. That was an exciting moment.’

“After Case gave his paper, Feynman got up and commented: ‘But what about Slotnick’s calculation? Your theorem must be wrong because a simple calculation shows that it’s correct. I checked Slotnick’s calculation and I agree with it.’

“He was of course turning the tables on Oppenheimer for his arrogant dismissal of Slotnick’s calculations. ‘I had fun with that,’ Feynman admits …

“The other dividend from the Slotnick episode was that Feynman learned the different kinds of meson theories and formulated the rules for calculating with them. In less than two months, during the spring of 1949, he recalculated … all the meson-theoretic calculations that had ever been performed up to that time – and many more. These efforts were summarized in the concluding paragraph of his ‘Space-time approach to quantum electrodynamics’ [*Physical Review* 76 (1949), 769-789]: ‘Calculations are very easily carried out to lowest order in [the coupling constant]] for the various theories for nucleon interaction, scattering of mesons by nucleons, meson production by nuclear collisions and by gamma rays, nuclear magnetic moments, neutron-electron scatterings, etc.’.” But Feynman gave no details of these calculations in the published article.

There was a major difference between QED and meson theories. “Most of the new particles [e.g., mesons] interacted *strongly*, unlike the weak electrodynamic interaction. If theorists tried to treat interactions among, for example, pions [a type of mesons] and protons in the same way as they treated electron-photon scattering, with a long series of more and more complicated Feynman diagrams, each containing more and more vertices, then each higher-order diagram would include extra factors of the large [coupling constant]. In contrast with the situation in QED, then, these complicated diagrams, with many vertices and hence many factors of [the coupling constant], would overwhelm the lowest-order, more basic contributions. Perturbative approaches seemed impossible within meson physics” (Kaiser, p. 58).

Feynman described his work on mesons in an interview with Charles Weiner at the AIP Center for the History of Physics (June 26, 1966): “I had work in trying to understand mesons, much of which is not published … I had done a lot of stuff after the electrodynamics on meson theory, to try to avoid the perturbation approximation and so on … I invented a number of methods to avoid perturbation theory, using the path integrals and operator calculus” (aip.org/history/ohilist/5020_4.html). These are the methods described in the present lecture notes. They make only limited use of Feynman diagrams. Indeed, Feynman wrote to Enrico Fermi from Brazil in December 19, 1951: “Don’t believe any calculation in meson theory which uses a Feynman diagram!” Elsewhere he referred to the field of meson physics by saying, “Perhaps there weren’t enough clues for even a human mind to figure out what is the pattern” (Krauss, p. 169).

Feynman delivered a second lecture course on meson theories, ‘High Energy Phenomena and Meson Theories,’ at Caltech the following year (January-March 1951), but after that his interests turned in a new intellectual direction, towards the problem of superfluidity.

*This Month at Caltech* (March 1950) notes (p. 14): “Dr. Richard P. Feynman, Professor of Theoretical Physics at Cornell University, delivered a series of twelve seminar lectures at the Institute last month on ‘Quantum Electrodynamics and Meson Theories.’ Dr. Feynman was the third in a series of eminent physicists to lecture at the Institute this year, following Drs. Rabi and Oppenheimer.” The lecture notes were recorded and printed by two Caltech graduate students: Carl W. Helstrom, who became one of the pioneers of quantum information theory, and Malvin A Ruderman, who is today on the faculty of Columbia University, where he specializes in “collapsed objects in astrophysics, especially neutron stars” (Columbia faculty bio).

Few copies of these notes have survived. In his comprehensive history of the invention and use of Feynman diagrams, *Drawing Theories Apart* (2005), David Kaiser refers (p. 432) to a copy of the notes in the possession of Sam Schweber as the only copy he has been able to consult.

Kaiser, ‘Making tools travel: pedagogy and the transfer of skills in post-war theoretical physics,’ in: *Pedagogy and the Practice of Science* (Kaiser, ed.), 2005. Krauss, *Quantum Man*, 2011. Schweber, *QED and the Men Who Made It*, 1994.

Mimeographed notes, printed on recto only, 4to (280 x 217 mm), pp. 81, numerous mathematical formulas and diagrams in text, including several Feynman diagrams (first two pages detached, title paged toned and with minor marginal chipping). Stapled as issued.

Item #5205

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Price:
$18,000.00
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