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Quantum theory: concepts and methods. (English) Zbl 0820.00011
Fundamental Theories of Physics. 57. Dordrecht: Kluwer Academic Publishers,. xiv, 446 p. (1993).
The book is devoted to the foundations of quantum theory but not to the philosophy of science. Its purpose is to clarify the conceptual meaning of the theory and to explain some of the mathematical methods. The author puts stress on the physical meaning attributed to abstract mathematical objects. The pragmatic and at the same time rigorous approach, inclusion of the latest developments, numerous exercises and bibliographical references as well as some computer programs make this graduate level textbook ideal for independent study.
The volume consists of 12 chapters grouped in three parts. The first part introduces the formal tools necessary for the study of quantum theory and defines the operational meaning of preparations and tests. The ill- defined notions like “quantum uncertainties” do not appear in presentation.
The central part of the book contains extensions of quantum theory using “hidden variables”. Nonlocal effects related to the Bell’s theorem and contextual effects related to the Kohen-Specker theorem are examined in detail. It is here that quantum phenomena depart most radically from classical physics.
The third part begins with the spacetime symmetries (Galilean and relativistic), then the author discusses topics belonging to the current research area, i.e. information theory and thermodynamcis (including quantum cryptography and “teleportation”), semiclassical methods, irreversibility questions and chaos. The final chapter contains analysis of the measuring process. It is shown how modern techniques allow to get more information from a physical system than traditional measurement methods. Opposite to the von Neumann’s approach, here the measuring process is represented by a non-orthogonal positive operator-valued measure.
It is worth noting that only the standard (generally accepted) quantum theory is treated in this book.

MSC:
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
81P15 Quantum measurement theory, state operations, state preparations
81P68 Quantum computation
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