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The Dirac Equation: Feynman’s Great Struggle

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The Genesis of Feynman Diagrams

Part of the book series: Archimedes ((ARIM,volume 26))

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Abstract

In this chapter I will show how Feynman used diagrams to represent and modify physical models of electrons (and later their interaction) and how he used these representations to derive quantitative expressions that are “true of the model”.

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Notes

  1. 1.

    Cartwright (1983).

  2. 2.

    Cf. Weisskopf (1939, p. 72); cf. also Feynman and Hibbs (1965), problem 2–6, p. 34, where the problem is presented as being made up for pedagogical purposes only and devoid of any relationship to a real physical situation.

  3. 3.

    Dirac (1935, p. 260).

  4. 4.

    Cf. Jacobson and Schulman (1984), Figure 1.

  5. 5.

    See, e. g., Galison (1998).

  6. 6.

    Dirac Equation a, folio 27.

  7. 7.

    Dirac Equation a (1946/47a, folio 1), (Feynman’s page numbering: 1), see Fig. 4.10; cf. Schweber (1994a, p. 406). Feynman’s letter was written on a “Monday February 10”. Around the time in question, February 10 was a Monday in 1941, 1947 and 1958. The content of the letter makes 1947 the most plausible date. This is also the date that Schweber assumes to be correct.

  8. 8.

    Dirac Equation a (1946/47a, folio 11 (page 10)), see Fig. 4.15.

  9. 9.

    Dirac Equation a (folio 1 (page 1)).

  10. 10.

    Dirac Equation a (folio 1 (page 1)).

  11. 11.

    Dirac Equation a, folio 2 (page 2), see Fig. 4.11, emph. in the original.

  12. 12.

    Dirac Equation a, folio 3 (page 3), see Fig. 4.12.

  13. 13.

    Dirac Equation a, folios 5 and 6 (pages 5 and 6) see Figs. 4.13 and 4.14.

  14. 14.

    Dirac Equation a, folios 12 and 14 (pages 11 and 12), see Figs. 4.16 and 4.17.

  15. 15.

    Dirac Equation a, folio 14 (page 12).

  16. 16.

    Dirac Equation a, folio 11 (page 10).

  17. 17.

    Dirac Equation a, folio 12 (page 11).

  18. 18.

    RMP48, p. 367.

  19. 19.

    Dirac Equation a, folio 12 (page 11).

  20. 20.

    Dirac (1935).

  21. 21.

    Dirac (1935, p. 297); quoted in Feynman (1966, p. 699).

  22. 22.

    Welton (2007, p. 46).

  23. 23.

    Dirac (1946).

  24. 24.

    Weiner (1966, p. 15), see also Schweber (1994, p. 405).

  25. 25.

    Dirac Equation a, folio 12 (page 11), emph. in the original.

  26. 26.

    Dirac Equation a, folio 16 (page 13, last page) see Fig. 4.18.

  27. 27.

    See, e. g., Dirac (1935, p. 270ff).

  28. 28.

    Feynman (1966, p. 706) (middle column), see also p. 702 (middle and right column), p. 705 (right column); see also Schweber (1994, pp. 387/388) and Weiner (1966a, p. 31/32).

  29. 29.

    In other words: let \(\chi_{AB}=ab\), where a contains the factors that correspond to the extremal turns and b the factors that correspond to the left/right turns. If each factor were replaced with its complex conjugate we would have \(\chi_{BA}=\chi_{BA}^{*}=a^{*}b^{*}\). Now, because the factors that correspond to the extremal turns are, in fact, not replaced with their complex conjugates, we have instead \(\chi_{BA}=ab^{*}=\frac{ab^{*}}{a^{*}b^{*}}a^{*}b^{*}\). Since a is a product of an odd number of is, we have \(a={\mathrm{e}}^{{\mathrm{i}}\frac{\pi}{2}(2n+1)}\), where n is an integer, and, therefore, \(\chi_{BA}={\mathrm{e}}^{{\mathrm{i}}\pi(2n+1)}a^{*}b^{*}=-\chi_{AB}^{*}\).

  30. 30.

    “Minutes of the Cambridge, Massachusetts, Meeting, February 21 and 22, 1941” 1941; Wheeler and Feynman (1945, 1949).

  31. 31.

    Feynman (2005, p. 5).

  32. 32.

    Feynman (2005, p. 31).

  33. 33.

    See Wheeler and Feynman (1949, p. 425).

  34. 34.

    See Wheeler and Feynman (1949), equation (1).

  35. 35.

    Feynman (2005, p. 10).

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  1. University of Bern, History and Philosophy of Science, Exact Sciences, Sidlerstrasse 5, 3012, Bern, Switzerland

    Adrian Wüthrich

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Wüthrich, A. (2010). The Dirac Equation: Feynman’s Great Struggle. In: The Genesis of Feynman Diagrams. Archimedes, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9228-1_4

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