Abstract
In the early 1940s, when Feynman was a graduate student, one of the most pressing problems facing theoretical physicists of the time was the fact that infinite and, therefore, uninterpretable quantities arose from some of the principles of electrodynamics—in both classical electrodynamics as well as in the early attempts to establish a quantum theory.1 Roughly, the problem was as follows: an extended electron could not be stable because the charges distributed over its volume would repel each other. On the other hand, a point-like electron would imply that the energy contained in the electron’s electrostatic field would be infinite, since the field energy e/r diverges in the limit of vanishing radius r of the spatial distribution of the charge e.2
But what does the quantum mechanician do if he cannot be provided with a Hamilton operator? He goes on strike.
Heinrich Leutwyler
Lecture notes ‘Elektrodynamik und Optik’ (p. 21)
Translation A. W.
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Notes
- 1.
For a comprehensive account of the history of QED, see Schweber (1994).
- 2.
- 3.
- 4.
Feynman (2005), Introduction.
- 5.
Only a summary of a presentation of Wheeler and Feynman’s theory had been published by the time Feynman started working on his thesis (see “Minutes of the Cambridge, Massachusetts, Meeting, February 21 and 22, 1941”, p. 683). The published accounts of the theory are Wheeler and Feynman (1945, 1949).
- 6.
Feynman (2005), Introduction.
- 7.
Dirac (1935, pp. 124–126).
- 8.
Quoted in Feynman (2005, p. 26).
- 9.
Weiner (1966b, p. 148–149), reprinted with permission. Copyright 1966, American Institute of Physics.
- 10.
- 11.
Feynman (2005, p. 28).
- 12.
Feynman (2005, p. 28).
- 13.
Feynman (2005, p. 31).
- 14.
Dirac (1935), equation 24, p. 125.
- 15.
Feynman (2005, p. 31).
- 16.
Feynman (2005), equation 47.
- 17.
Feynman (2005, p. 69).
- 18.
Cf. equation 62 in Feynman (2005, p. 39).
- 19.
Feynman (2005), equation 61.
- 20.
Cf. equation 50 in Feynman (2005, p. 32).
- 21.
RMP48, p. 367.
- 22.
Feynman (2005, p. 41); Feynman writes \(\mathcal{A}\) instead of S for the action.
- 23.
RMP48, p. 374.
- 24.
RMP48, p. 375.
- 25.
RMP48, p. 376.
- 26.
Schwinger (1948b).
- 27.
For a more extended account of Schwinger’s and Feynman’s biographies and their contributions to QED, see Schweber (1994, chapters 7 and 8).
- 28.
Pauli (1933, p. 237).
References
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Wüthrich, A. (2010). Quantum Mechanics Without a Hamiltonian Operator. In: The Genesis of Feynman Diagrams. Archimedes, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9228-1_3
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