The Logic of Quantum Mechanics: Volume 15

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Originally published in 1981, this book forms volume 15 of the Encyclopedia of Mathematics and its Applications. The text provides a clear and thorough treatment of its subject, adhering to a clean exposition of the mathematical content of serious formulations of rational physical alternatives of quantum theory as elaborated in the influential works of the period, to which the authors made a significant contribution. The treatment falls into three distinct, logical parts: in the first part, the modern version of accumulated wisdom is presented, avoiding as far as possible the traditional language of classical physics for its interpretational character; in the second part, the individual structural elements for the logical content of the theory are laid out; in part three, the results of section two are used to reconstruct the usual Hilbert space formulation of quantum mechanics in a novel way.

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Editorial Reviews

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Review of the hardback: ' … this elegant and very sophisticated work is directed to those mathematicians and theoretical physicists with special interest in the logical consistency and mathematical content of the physical principles of quantum mechanics … It is well-referenced, and the reader who perseveres in studying the book will be amply rewarded'. Choice
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Product Details

Table of Contents

Editor's statement; Foreword; Preface; Part I. Hilbert-Space Quantum Mechanics; 1. Static description of quantum mechanics; 2. States; 3. Physical quantities; 4. Spin and motion; 5. Superselection rules; 6. Dynamical evolution; 7. Compound systems; 8. Elementary analysis of the measurement process; 9. Mathematical structures emerging from the Hilbert-Space formulation of Quantum mechanics; Part II. Basic Structures in the Description of Quantum Mechanics; 10. The typical mathematical structure of propositions: orthomodular AC lattices; 11. Probability measures on orthomodular posets and lattices; 12. Characterization of commutativity; 13. States and propositions of a physical system; 14. Quantum-mechanical features in terms of the logic of the physical system; 15. On the hidden-variable issue; 16. Proposition-state structure and idealized measurements; 17. Superpositions of states and closure spaces; 18. Transition-probability spaces and quantum systems; 19. On the convex-set approach; 20. Introduction to a quantum logic; Part III. Reconstruction of Hilbert-Space Quantum Mechanics; 21. The coordinatization problem; 22. Use of real and quaternionic Hibert Spaces: a simple example; 23. Dynamics; 24. Composition of physical systems; 25. Hidden-variable theories and Gleason's Theorem; 26. Introduction to quantum probability theory; Appendices; Subject index.

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