Mathematical Foundations of Quantum Theory

Mathematical Foundations of Quantum Theory

1st Edition - January 28, 1978

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  • Editor: A.R. Marlow
  • eBook ISBN: 9780323141185

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Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.

Table of Contents

  • List of Contributors


    The Mathematical Foundations of Quantum Theory

    The "Past" and the "Delayed-Choice" Double-Slit Experiment

    The Lorentz Particles: A New Model for the ½-Spin Particle and the Hydrogen Atom

    Orthomodular Structures and Physical Theory

    Another Nonstandard Quantum Logic (and How I Found It)

    Some Unsolved Problems in Quantum Logics

    Manuals, Morphisms, and Quantum Mechanics

    Limits of Manuals and Logics

    The Geometry of the State Space

    Spin Manuals: Empirical Logic Talks Quantum Mechanics

    The State of the Pentagon: A Nonclassical Example

    The Nikodym-Hahn-Vitale-Saks Theorem for States on a Quantum Logic

    On Geometric Quantization of Classical Systems

    Measures with Minimum Uncertainty on Non-Commutative Algebras with Application to Measurement Theory in Quantum Mechanics

    Duality for C*-Algebras

    Geometrodynamics as Foundation of Physics

    Spin and Statistics of Elementary Particles

    Quantum Mechanics with Density Operators

    Pure States, Mixtures, and Compounds

    Position and Momentum Distributions Do Not Determine the Quantum Mechanical State

Product details

  • No. of pages: 382
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: January 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9780323141185

About the Editor

A.R. Marlow

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