Dubin, D. A.; Hennings, M. A. Quantum mechanics, algebras and distributions. (English) Zbl 0705.46039 Pitman Research Notes in Mathematics, 238. Harlow: Longman Scientific & Technical; New York: John Wiley & Sons, Inc. 238 p. £19.50 (1990). 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 Cited in 16 Documents 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 PDFBibTeX XMLCite \textit{D. A. Dubin} and \textit{M. A. Hennings}, Quantum mechanics, algebras and distributions. Harlow: Longman Scientific \&| Technical; New York: John Wiley \&| Sons, Inc. (1990; Zbl 0705.46039)