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The magic of Feynman’s QED: from field-less electrodynamics to the Feynman diagrams

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Abstract

For some time, even after the Feynman diagrams and rules were publicly known, the foundations of Feynman’s quantum electrodynamics remained mostly private. Its stupendous efficiency then appeared like magic to most of his competitors. The purpose of this essay is to reveal the hidden contrivances of this magic, in a journey from field-less electrodynamics to the Feynman diagrams.

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References

  1. Bethe, Hans. 1947. The electromagnetic shift of energy levels.Physical Review, 72: 339–341

    Article  ADS  Google Scholar 

  2. Blum, Alexander. 2017. The state is not abolished, it withers away: How quantum field theory became a theory of scattering.Studies in History and Philosophy of Modern Physics, 60: 46–80

    Article  ADS  MathSciNet  Google Scholar 

  3. Cahill, Kevin. 2013.Physical mathematics. Cambridge: Cambridge University Press

  4. Darrigol, Olivier. 1982.La genèse du concept de champ quantique. Thèse de doctorat, Université de Paris 1-Sorbonne. http://www.sphere.univ-paris-diderot.fr/IMG/pdf/Darrigol_Genese_cropped2.pdf

  5. Darrigol, Olivier. 1988. Elements of a scientific biography of Tomonaga Sin-Itiro.Historia Scienciarum, 35: 1–29

    MathSciNet  Google Scholar 

  6. Darrigol, Olivier. 2009. Stueckelberg’s united field-theory of matter, 1936–39. In Jan Lacki, Henri Ruegg, and Gerar Wanders (eds.),E.C.G. Stueckelberg, an unconventional figure of twentieth century physics. Selected scientific papers with commentaries (Berlin: Springer, 2009)

  7. Dirac, Paul. 1933. The Lagrangian in quantum mechanics.Physikalische Zeitschrift der Sowietunion, 3: 64–72

    MATH  Google Scholar 

  8. Dirac, Paul. 1938. Classical theory of radiating electrons.Proceedings of the Royal Society of London, A167: 148–169

    ADS  MATH  Google Scholar 

  9. Dyson, Freeman. 1949a. The radiation theories of Tomonaga, Schwinger, and Feynman.Physical Review, 75: 486–502

    Article  ADS  MathSciNet  Google Scholar 

  10. Dyson, Freeman. 1949b. The S matrix in quantum electrodynamics.Physical Review, 75: 1736–1755

    Article  ADS  MathSciNet  Google Scholar 

  11. Eigner, Kai, and Frans van Lunteren. 2011. ‘The shackles of causality’: Physics and philosophy in the Netherlands in the interwarperiod. In Alexei Kojevnikov, Cathryn Carson, and Helmuth Trischler (eds.),Weimar culture and quantum mechanics: Selected papers by Paul Forman and contemporary perspectives on the Forman thesis (Singapore: World Scientific), pp. 375–396

  12. Feynman, Richard. 1942. The principle of least action in quantum mechanics. PhD, Princeton University. Also in Laurie Brown (ed.),Feynman’s thesis: A new approach to quantum theory (Singapore: Word Scientific, 2005)

  13. Feynman, Richard. 1948a. Space-time approach to non-relativistic quantum mechanics.Reviews of Modern Physics, 20: 367–387

    Article  ADS  MathSciNet  Google Scholar 

  14. Feynman, Richard 1948b A relativistic cut-off for classical electrodynamics.Physical Review, 74: 939–946

    Article  ADS  MathSciNet  Google Scholar 

  15. Feynman, Richard. 1948c. Relativistic cut-off for quantum electrodynamics.Physical Review, 74: 1430–1438

    Article  ADS  MathSciNet  Google Scholar 

  16. Feynman, Richard. 1949a. The theory of positrons.Physical Review, 76: 749–769

    Article  ADS  Google Scholar 

  17. Feynman, Richard. 1949b. Space-time approach to quantum electrodynamics.Physical Review, 76: 769–789

    Article  ADS  MathSciNet  Google Scholar 

  18. Feynman, Richard. 1950. Mathematical formulation of the quantum theory of electromagnetic interaction.Physical Reveiw, 80: 440–457

    Article  ADS  MathSciNet  Google Scholar 

  19. Feynman, Richard. 1951 An operator calculus having application in quantum electrodynamics.Physical Review, 84: 108–128

    Article  ADS  MathSciNet  Google Scholar 

  20. Feynman, Richard. 1966. The development of the space-time view of quantum field theory. Nobel lecture, reprinted inPhysics Today, 1966, pp. 31–44

    Article  Google Scholar 

  21. Feynman, Richard, and John Archibald Wheeler. 1941. Reaction of the absorber as the mechanism of radiation damping.Abstract. Physical Review, 59: 682

    Google Scholar 

  22. Fokker, Adriaan. 1932. Théorie relativitiste de l’interaction de deux particules chargées.Physica, 12: 145–152

    MATH  Google Scholar 

  23. Galison, Peter. 1998. Feynman’s war: Modelling weapons, modelling nature.Studies in History and Philosophy of Modern Physics, 29: 391–434

    Article  ADS  MathSciNet  Google Scholar 

  24. Gleick, James. 1992.Genius: The life and science of Richard Feynman. New York: Pantheon Books

  25. Heisenberg, Werner. 1938. Die Grenzen der Anwendbarkeit der bisherigen Quantentheorie.Zeitschrift für Physik, 110: 251–266

    Article  ADS  Google Scholar 

  26. Kaiser, David. 2005.Drawing theories apart: The dispersion of Feynman diagrams in postwar physics. Chicago: The University of Chicago Press

  27. Lacki, Jan. 2004. The puzzle of canonical transformations in early quantum mechanics.Studies in History and Philosophy of Modern Physics, 35: 317–344

    Article  ADS  MathSciNet  Google Scholar 

  28. Sauer, Tilman. 2008. Remarks on the origins of path integration: Einstein and Feynman. https://arXiv:0801.1654.

  29. Schweber, Silvan. 1994.QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga. Princeton: Princeton University Press

  30. Schwinger, Julian. 1948a. On quantum-electrodynamics and the magnetic moment of the electron.Physical Review, 73: 416–417

    Article  ADS  Google Scholar 

  31. Schwinger, Julian. 1948b. Quantum electrodynamics. Pt. 1: A covariant formulation.Physical Review, 74: 1439–1461

    Article  ADS  MathSciNet  Google Scholar 

  32. Schwinger, Julian. 1949. Quantum electrodynamics. Pt. 2: Vacuum polarization and self-energy. Physical Review, 75: 651–679

    MATH  Google Scholar 

  33. Tomonaga, Sin-itiro. 1946. On a relativistic invariant formulation of the quantum theory of wave fields.Progress in Theoretical Physics, 1: 27–42

    Article  ADS  Google Scholar 

  34. Tomonaga, Sin-itiro. 1948. On infinite reactions in quantum field theory.Physical Review, 74: 224–225

    Article  ADS  Google Scholar 

  35. Wanders, Gérard. 2009. Stueckelberg and the S-Matrix theory. In Jan Lacki, Henri Ruegg, and Gérard Wanders (eds.),E.C.G. Stueckelberg, an unconventional figure of twentieth century physics (Basel: Birkhäuser), 87–100

  36. Wheeler, John Archibald. 1979. Some men and moments in elementary particle research. In Roger Stuewer (ed.),Nuclear physics in retrospect: Proceeding of a symposium on the 1930s. (Minneapolis: University of Minnesota Press), 213–324

  37. Wheeler, John Archibald, and Richard Feynman. 1945. Interaction with the absorber as the mechanism of radiation.Reviews of Modern Physics, 17: 157–181

    Article  ADS  Google Scholar 

  38. Wheeler, John Archibald, and Richard Feynman. 1949. Classical electrodynamics in terms of direct interparticle action.Reviews of Modern Physics, 21: 425–433

    Article  ADS  MathSciNet  Google Scholar 

  39. Wüthrich, Adrian. 2010.The genesis of Feynman diagrams. Heidelberg: Springer

  40. Wüthrich, Adrian. 2012. Interpreting Feynman diagrams as visual models.Spontaneous Generations: A Journal for the History and Philosophy of Science, 6: 172–181

    Google Scholar 

  41. Wüthrich, Adrian. 2013. Against the impossible picture: Feynman’s heuristics in his search for a divergence-free quantum electrodynamics.Physics and Philosophy. http://hdl.handle.net/2003/29919, Article ID 019

  42. Wüthrich, Adrian. 2018. The exigencies of war and the stink of a theoretical problem: Understanding the genesis of Feynman’s quantum electrodynamics as mechanistic modeling at different levels.Perspectives on Science, 26: 501–520

    Article  Google Scholar 

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Darrigol, O. The magic of Feynman’s QED: from field-less electrodynamics to the Feynman diagrams. EPJ H 44, 349–369 (2019). https://doi.org/10.1140/epjh/e2019-100025-2

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  • DOI: https://doi.org/10.1140/epjh/e2019-100025-2

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