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The Logic of Quantum Mechanics

The Logic of Quantum Mechanics

Volume 15

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: December 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521168496


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About the Authors
  • 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.

    Reviews & endorsements

    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

    • Date Published: December 2010
    • format: Paperback
    • isbn: 9780521168496
    • length: 336 pages
    • dimensions: 234 x 156 x 18 mm
    • weight: 0.47kg
    • availability: Available
  • Table of Contents

    Editor's statement
    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
    Subject index.

  • Authors

    Enrico G. Beltrametti, University of Genoa

    Gianni Cassinelli, Università degli Studi di Genova


    Gian-Carlo Rota


    Peter A. Carruthers, Los Alamos National Laboratory

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