On the work of Edward Witten. (English) Zbl 0742.01013

Atiyah, Michael

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 31-35 (1991).

[For the entire collection see Zbl 0741.00019.]
Address in the event of the Fields Medal awarding to E. Witten. As the best of his ideas the following are pointed out: supersymmetric quantum field theory as the Hodge-de Rham theory of infinite-dimensional manifolds, anomalies from the global point of view, the index theorem for the Dirac operator on compact manifolds emerged by a formally exact functional integral on the loop space. The following achievement of E. Witten are shortly characterized: the new proof of the positive energy theorem in general relativity based on linear P.D.E. and supergravity ideas, new rigidity theorems based on the infinite sequence of operators and Feynman path integral, topological quantum field theories (in particular, the Jones invariants of knots as Feynman integrals for a 3- dimensional gauge theory).

Reviewer: Ü.Lumiste (Tartu)

MSC:

01A60	History of mathematics in the 20th century
01A70	Biographies, obituaries, personalia, bibliographies

Keywords:

Hodge-de Rham theory; compact manifolds; general relativity; supergravity ideas

Citations:

Zbl 0741.00019