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Logarithmic divergence of electron self-energy and charge renormalization — Weisskopf

1939 AD · Transmission: Global
PhysicsTheoryNorth American

Victor Weisskopf, now at the University of Rochester after fleeing Nazi Europe with Niels Bohr's help, revisits in 1939 a problem he had first tackled five years earlier, in 1934, as Pauli's assistant in Zurich: calculating the electron's self-energy — the energy associated with the electron's interaction with its own electromagnetic field. In that first attempt he made a sign error, spotted by a then little-known physicist at Harvard, Wendell Furry; once corrected, the result showed that the self-energy diverged only logarithmically, in sharp contrast with the linear divergence of classical electrodynamics and the quadratic divergence obtained in a simpler (positron-free) version of quantum theory. When showing the error to Pauli, Weisskopf anxiously asked whether he should give up physics; Pauli, with his characteristic dryness, simply replied: "I never make mistakes." In "On the Self-Energy and the Electromagnetic Field of the Electron" (Physical Review, 1939), Weisskopf extends and rigorously proves that result: he shows that, thanks to Dirac's positron theory — the contributions of virtual electron-positron pairs cancel much of the divergence that would otherwise appear — the self-energy is only logarithmically infinite, and that this result holds to all orders in an expansion in powers of the fine-structure constant, not just in the first approximation. Crucially, Weisskopf clearly recognizes that this remaining infinity, though mathematically present, could be absorbed into a redefinition — a renormalization — of the electron's observed mass and charge, without affecting the theory's verifiable physical predictions. This early recognition of the idea of charge and mass renormalization, a decade before Freeman Dyson generalized the concept to full quantum electrodynamics (1949, see separate entry dyson-qed-equivalence-renormalization-1949), is the specific contribution for which Weisskopf, together with Dyson and 't Hooft, would receive the shared 1981 Wolf Prize in Physics.

InstitutionUniversity of Rochester, New York
Historical regionUnited States
Primary sourceWeisskopf, V. F. — "On the Self-Energy and the Electromagnetic Field of the Electron" (Physical Review, 56, 72-85, July 1, 1939). DOI: 10.1103/PhysRev.56.72
Secondary sourceJackson, J. D. & Gottfried, K. — "Victor Frederick Weisskopf" (National Academy of Sciences, Biographical Memoirs, vol. 84, doi: 10.17226/10992); Schweber, S. S. — "A Critical History of Renormalization" (arXiv:1310.5533); Wolf Foundation — "Victor J. Weisskopf" (wolffund.org.il)
Original languageEnglish
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