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Mathematics motivated by physics. (English) Zbl 0715.46036
The legacy of John von Neumann, Proc. Summer Res. Inst., Hempstead/NY (USA) 1988, Proc. Symp. Pure Math. 50, 137-150 (1990).
[For the entire collection see Zbl 0699.00010.]
Following the spirit of von Neumann, the author describes some results in analysis and geometry of infinite dimensional manifolds, including \(P(\phi)_ 2\) theory and supersymmetric models which do not require renormalization in constructive field theory, the supersymmetry in the latter model, the index theory associated with it, the KMS property and the entire cyclic cohomology.
In the last section, the author criticizes recent trends of some theoretical physicists, producing works which the author considers to be neither physics nor mathematics.
Reviewer: H.Araki
46L60 Applications of selfadjoint operator algebras to physics
46N50 Applications of functional analysis in quantum physics
81T08 Constructive quantum field theory
Zbl 0699.00010