Mathematical Foundations of Quantum Theory

Mathematical Foundations of Quantum Theory

by A.R. Marlow

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Overview

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.

Product Details

ISBN-13: 9780323141185
Publisher: Elsevier Science
Publication date: 12/02/2012
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 382
File size: 5 MB

Table of Contents

List of Contributors

Preface

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


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