Abstract
Richard Feynman (1918–1988) is probably the most brilliant theoretical physicist of the second half of 20th century. In his work at Princeton under the direction of John Archibald Wheeler, Feynman sought to solve the problem of divergent expressions in quantum field theory, which, together with Julian Schwinger and Sin-Itiro Tomonaga, was the reason of their award of the 1965 Nobel Prize in Physics “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles”, This has had profound consequences for particle physics. The theory of the Renormalization Group has since revealed a depth that guides the theoretical physics of contemporary elementary particles.
You can never solve a problem
on the level on which is was created.
Albert Einstein
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Notes
- 1.
John Archibald Wheeler and Richard Phillips Feynman, Interaction with the Absorber as the Mechanism of Radiation, Rev. Mod. Phys. 17, 157, 1945.
- 2.
At a beer party in the Nassau Tavern at Princeton. The account of this event can be found in Feynman’s Nobel Conference, https://www.nobelprize.org/prizes/physics/1965/feynman/lecture/.
- 3.
P.A.M. Dirac, Physikalische Zeitschrift der Sowjetunion 3, No. 1 (1933).
- 4.
R. P. Feynman, The principle of least action in quantum mechanics, Ph. D. thesis, Princeton University, 1942; Space-Time approach to Non-Relativistic Quantum Mechanics, Rev. Mod. Phys, vol. 20, p. 367, 1948: see also [26].
- 5.
The exact and tasty words of the dialogue are reported by Feynman in his Nobel Prize-winning address.
- 6.
Common term due to Feynman, in field theory, for a Green’s function.
- 7.
This dialogue is narrated by Silvan S. Schweber, Feynman’s visualization of space-time processes, Review of Modern Physics, vol. 58, no. 2, 1 April 1986, pp. 449–508.
- 8.
P. A. M. Dirac, On the Analogy Between Classical and Quantum Mechanics Rev. Mod. Phys. 17, 195, 1945.
- 9.
Feynman’s Thesis; A new approach to Quantum Theory: The Principle of Least Action in Quantum Mechanics, Laurie M. Brown (Editor), World Scientific, Singapore, (2005).
- 10.
R. P. Feynman emphSpace-Time Approach to Non-relativistic Quantum Mechanics, Rev. Mod. Phys. 20,367 (1948).
- 11.
J. Schwinger, Phys. Rev. 82, 914 (1951).
- 12.
Of course, it is only after we have understood the physical and mathematical structure of the problem that this claim appears justified in good approximation.
- 13.
See, for instance, [11], Chap. 2, Sect. 6, for a discussion of this point.
- 14.
See, for instance, [11], Chap. 2, Sect. 1.
- 15.
Feynman added, with his legendary sense of humor, “The effect of the entire History on the future of the universe could be obtained from a single gigantic wave function.”
- 16.
R. P. Feynman, An operator Calculus Having Applications in Quantum Electrodynamics, Phys. Rev., vol 84, pp. 108–128, 1951.
- 17.
See also Lawrence Schulman, A Path Integral for Spin, Phys. Rev. 176, 1558, 1968; and the remarkable analysis of Alexander Altman, Ben D. Simons, Condensed matter field Theory, Cambridge University Press, (2010) Chap. 3, 134.
- 18.
D. M. Greenberger, M. Horne, and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos, (Kluwer, Dordrecht, 1989); D. M. Greenberger, M. Horne, and A. Zeilinger Going Beyond Bell’s Theorem, arXiv:0712.0921v1 [quant-ph] 2007; D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, Bell’s theorem without inequalities, Am. J. Phys. \( \textbf{58}\), 1131 (1990); N. D. Mermin, Phys. Today \(\textbf{43}\) (6).9 (1990).
- 19.
Jian-Wei Pan, D. Bouwmeester, M. Daniell, H. Weinfurter and A. Zeilinger, Experimental test of quantum nonlocality in three photon GHZ entanglement, Nature, \(\textbf{403}\) (6769), 515 (2000); Jian-Wei Pan and Anton Zeilinger, (2002) Multi-Photo Entanglement and Quantum Non-Locality https://vcq.quantum.at/fileadmin/Publications/2002-12.pdf.
- 20.
Julian Schwinger, Phys. Rev. 82, 914 (1951).
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Basdevant, JL. (2023). Feynman’s Path Integrals in Quantum Mechanics. In: Variational Principles in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-21692-3_9
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