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Title: Irreversibility and Causality: Semigroups and Rigged Hilbert Spaces: A Selection of Articles Presented at the 21st International Colloquium on Group Theoretical Methods in Physics (Lecture Notes in Physics, 504) by International Colloquium on Group Theoretical Methods in Physics 1996, Arno Bohm, H. D. Doebner, P. Kielanowski ISBN: 3-540-64305-2 Publisher: Springer Verlag Pub. Date: June, 1998 Format: Paperback Volumes: 1 List Price(USD): $77.95

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Average Customer Rating: 5 (1 review)

Rating: 5
Summary: Bohm et al.'s Irreversibility and Causality
Comment: Professor David Ruelle of France has a whole chapter on irreversibility in his book Chance and Chaos (see my review). Ievitably increasing entropy (disorder) is an example of an irreversible phenomenon, according to thermodynamics. The present book's editors are mostly from the University of Texas and Mexico. They have done an outstanding job in identifying the errors in the old Hilbert space formulation of quantum mechanics, including the facts that neither plane waves nor delta functions are finitely square integrable (the reader can think of this roughly as a lack of finiteness property) and neither are the eigenvectors of points of the continuous spectrum of self-adjoint operators (self adjoint operators are mathematical descriptions of things that can be observed in physics as opposed to only "theoretical" or even non-observable objects, which descriptions themselves are criticized by one of the authors in the book, Antoine of Belgium, as involving nonmathematical operational content). Also, Hilbert spaces (HS for short) cannot support unsmeared field operators and in general very singular operators (they end up with domain zero). Separable HSs are isomorphic (this means roughly that they correspond algebraically or mathematically to each other very exactly), but quantum systems supposedly described by them turn out not to be. There is only time here to say that this book and the papers on which it was based essentially remedied the problem by expanding Hilbert spaces to slightly more general spaces, which was an ingenious achievement. However, I believe that they may have to be expanded more severely to Banach spaces (which I may discuss in a later review of the book). Readers unfamiliar with the mathematics should hire reputable consultants or tutors to translate the book into a closer approximation to English, in order to keep up with one of the most important areas of quantum theory and to hopefully learn to use similar techniques in their own fields when needed.