June 20, 2018

CRM/Fields Institute Prize Lecture 2000
Given by
Israel Michael Sigal, University of Toronto
October 30, 2000

Some Mathematical Problems of Quantum Field Theory
In this talk I will describe some analytical problems in Quantum Field Theory (QFT) and some of the recent results and approaches. I will not assume any prior knowledge of the subject and I will try to show how it arises from Classical Field Theory, i.e. partial differential equations. In other words I will view QFT as Quantum Mechanics of infinitely many degrees of freedom or of extended objects (strings, surfaces, etc).

See Canadian Mathematical Society notes.


Israel Michael Sigal is one of the leading experts in the mathematical analysis of non-relativistic quantum theory worldwide. His theorem with Soffer on the N-body problem provided a completely rigorous solution to a major unsolved problem due to Schroedinger and was critical in establishing a firm mathematical foundation for quantum mechanics. His recent contributions to quantum electrodynamics provide a consistent mathematical description of the theory proposed by Feynmann, Schwinger and Tomonaga and represents a revolutionary approach to the subject. Professor Sigal received his bachelor's degree from Gorky University and his doctorate from Tel-Aviv University. Among his many honours, he has given addresses at the International Congress on Mathematical Physics and International Congress of Mathematics. He is a Fellow of the Royal Society of Canada and received the John L. Synge Award for outstanding work by a Canadian mathematician in 1993. He is an editor of the Duke Mathematical Journal and Reviews in Mathematical Physics. He is currently a University Professor and holds the Norman Stuart Robinson Chair at the University of Toronto.