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Quantum mechanics, algebras and distributions. (English) Zbl 0705.46039

As the authors state in their introduction: “Both quantum mechanics and statistical mechanics share the notable property that an understanding of the theory lies rather deep, yet a mastery of the associated calculations is quite straightford”. I would not totally adhere to the last statement even though the first one would certainly be agreed by all practitioners.
The volume under review is mostly a mathematical analysis of the tools mostly from functional analysis and operator theory, necessary for a consistent axiomatization of nonrelativistic elementary quantum mechanics. As those cover quite a large spectrum one should congratulate the authors for having given a fairly thorough and up to date presentation in slightly more than two hundred pages supplemented by a large number of references.
Any serious student of the foundations of quantum mechanics with a strong mathematical inclination will find the present volume of great interest.
Reviewer: C.Itzykson

MSC:

46N50 Applications of functional analysis in quantum physics
47N50 Applications of operator theory in the physical sciences
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
46F10 Operations with distributions and generalized functions
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