Wikinventia — Atlas of discoveries and inventions · Global Age

Founding of topological quantum field theory — Edward Witten

1988 AD · Transmission: Global
MathematicsTheoryNorth American

Edward Witten publishes in 1988, in Communications in Mathematical Physics, the paper "Topological Quantum Field Theory", where he formulates a twisted version of supersymmetric gauge theory in four dimensions whose sole physical content consists of purely topological invariants, with no local degrees of freedom. The model provides the physical interpretation — previously speculated by Michael Atiyah but never formalized — of Donaldson invariants in 4-manifolds (Simon Donaldson, Fields Medal 1986), unexpectedly connecting theoretical physics with low-dimensional differential topology. Witten would formulate that same year two additional topological field theories, the topological sigma model in two dimensions and Chern-Simons theory in three, and the following year (1989) would reinterpret the Jones invariants in knot theory (Vaughan Jones, Fields Medal 1990) as Feynman path integrals. Witten received the Fields Medal in 1990, the first physicist to obtain it, but for the broad body of his work in mathematical physics, not for a single isolated milestone; in Wikinventia's editorial classification for Fields entries, this led to his being excluded as a prize-based entry (the same criterion applied to Kodaira, Grothendieck, or Mumford), although the 1988 paper does constitute, on its own merits, a citable, pinpointable milestone that warrants an independent entry.

InstitutionInstitute for Advanced Study, Princeton
Historical regionUSA
Primary sourceWitten, E. — "Topological quantum field theory" (Communications in Mathematical Physics, 117, 1988, pp. 353-386). DOI: 10.1007/BF01223371
Secondary sourceWikipedia — Topological quantum field theory / Edward Witten
Original languageEnglish
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