The logic of quantum mechanics
著者
書誌事項
The logic of quantum mechanics
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 15 . Section,
Cambridge University Press, 2010
- : paperback
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注記
Includes bibliographies and index
内容説明・目次
内容説明
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.
目次
- 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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