The Logic of Quantum Mechanics: Volume 15

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

Enrico G. Beltrametti (Author), Gianni Cassinelli (Author), Gian-Carlo Rota (Edited by), Peter A. Carruthers (Foreword by)

9780521168496, Cambridge University Press

Paperback, published 9 December 2010

336 pages
23.4 x 15.6 x 1.8 cm, 0.47 kg

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

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.

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.

Subject Areas: Mathematical foundations [PBC]