The Logic of Quantum Mechanics

This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.

Zusammenfassung
Originally published in 1981, this book forms volume 15 of the Encyclopedia of Mathematics and its Applications. The text provides a clean exposition of the mathematical content of serious formulations of rational physical alternatives of quantum theory, to which the authors made a significant contribution.

Inhalt
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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