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Half-sided modular inclusions and structure analysis in quantum field theory. (English) Zbl 0909.46062

Doplicher, S. (ed.) et al., Operator algebras and quantum field theory. Proceedings of the conference dedicated to Daniel Kastler in celebration of his 70th birthday, Accademia Nazionale dei Lincei, Roma, Italy, July 1–6, 1996. Cambridge, MA: International Press. 589-608 (1997).
One of the most important problem in contemporary theoretical physics is to establish criteria discriminating physically acceptable theories from those burdened with too many mathematically permitted manipulations. The well-known nuclearity condition of Buchholtz and Wichman is insufficient, because by using the continuous tensor product one can construct from good theories, satisfying nuclearity conditions, theories violating such conditions. The problem of constructing new good theories from a given one is far from being a trivial step.
The author is trying to develop suitable technics for the imbedding von Neumann subalgebras by using the concept of half-sided modular inclusions developed by himself.
The paper is a valuable contribution to the deep understanding of the mathematical basis of modern quantum field theory.
For the entire collection see [Zbl 0889.00022].

MSC:

46N50 Applications of functional analysis in quantum physics
46L60 Applications of selfadjoint operator algebras to physics
81T05 Axiomatic quantum field theory; operator algebras
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