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In retrospect

Nobel 1965: to infinity and beyond

Nature Reviews Physics volume 7, page 532 (2025)Cite this article

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The 1965 Nobel Prize in Physics was shared by Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles”. The three physicists had, independently, created a solid relativistic theory of quantum electrodynamics (QED). Each had conquered the problem in their own style — and the diversity of those styles is apparent in their lectures prepared for the Nobel ceremony. Rarely has a set of co-winners presented such diverging commentary on a winning work.

Over the next few years, Tomonaga worked out how to deal with that infinity, building on the idea of his colleague Shoichi Sakata (and, unknowingly, of Abraham Pais in the USA) that another infinite yet negative mass term (Sakata called it a ‘cohesive force’) could cancel the electromagnetic mass. Ultimately, inspired by some pre-war work by Sidney Dancoff and using the method of contact transformations, Tomonaga was able to conclude that “all infinities appearing in the scattering process can be attributed to either the infinity of the electromagnetic mass or to the infinity appearing in the electric charge — there are no other divergences in the theory,” which “is a very pleasant thing”; the infinite mass and infinite charge are readily controlled through renormalization.

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References

Original articles

  • Tomonaga, S. On a relativistically invariant formulation of the quantum theory of wave fields. Prog. Theor. Phys. 1, 27–42 (1946)

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  • Koba, Z., Tati, S. & Tomonaga, S. Prog. Theor. Phys. 2, 101–116 (1947)

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  • Schwinger, J. Quantum electrodynamics I. A covariant formulation. Phys. Rev. 74, 1439–1461 (1948)

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  • ibid. 75, 651–672 (1949)

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  • Feynman, R. P. Space-time approach to quantum electrodynamics. Phys. Rev. 76, 769–789 (1949)

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  1. Nature Reviews Physics https://www.nature.com/natrevphys/

    Alison Wright

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  1. Alison Wright
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Correspondence to Alison Wright.

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Wright, A. Nobel 1965: to infinity and beyond. Nat Rev Phys 7, 532 (2025). https://doi.org/10.1038/s42254-025-00877-7

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