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.
Biography:
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.
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