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).
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.