After reviewing the basic mathematics of quantum mechanics I will explain what a von Neumann algebra is and why it is as natural and necessary for understanding the quantum world as manifolds are for the classical world. An attempt to base quantum field theory on von Neumann algebras has, in the last 30 years, been extraordinarily successful in low dimensions. I will discuss a few of the high points of this theory.
Back to Workshop II: Approximation Properties in Operator Algebras and Ergodic Theory
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