Operator Algebras and Quantum Field Theory

Description

The book originated in the work of von Neumann, particularly in his search for a natural mathematical framework for quantum mechanics, and in the work of Gelfand and Naimark. The disciplines in which they worked can now be seen as encompassing noncommutative analysis, geometry, and topology. After the seminal work and ideas of Haag in the 1950s, and of Araki, Haag, and Kastler in the early 1960s, the original link with quantum mechanics evolved into a much deeper relation with quantum field theory—an instance of the mutual interaction and motivation between pure mathematics and mathematical physics.

The field of operator algebras is notable for the depth of its problems, the richness of its new ideas, connections with such a variety of other fields of mathematical study, and potential as a unifying language and source of illumination.

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