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Quantum axiomatics and nonassociative normed algebras. (Axiomatique quantique et algèbres normées non associatives.) (French) Zbl 0854.46059

The paper has an expository character. It presents an interesting discussion on the axiomatization of quantum mechanics. Different approaches are compared, in particular, the traditional setting where observables are represented by selfadjoint operators on a Hilbert space and the axiomatization where observables are represented by the elements of an abstract Jordan Banach algebra. The author concludes that Jordan Banach algebras are the most natural and convenient mathematical systems for quantum theory.

MSC:

46N50 Applications of functional analysis in quantum physics
46L70 Nonassociative selfadjoint operator algebras
81P05 General and philosophical questions in quantum theory
46L60 Applications of selfadjoint operator algebras to physics
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References:

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