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The Logic of Quantum Mechanics : Volume 15 - Enrico G. Beltrametti

The Logic of Quantum Mechanics

Volume 15

Paperback

Published: 9th December 2010
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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.

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

Editor's statement
Foreword
Preface
Hilbert-Space Quantum Mechanics
Static description of quantum mechanics
States
Physical quantities
Spin and motion
Superselection rules
Dynamical evolution
Compound systems
Elementary analysis of the measurement process
Mathematical structures emerging from the Hilbert-Space formulation of Quantum mechanics
Basic Structures in the Description of Quantum Mechanics
The typical mathematical structure of propositions: orthomodular AC lattices
Probability measures on orthomodular posets and lattices
Characterization of commutativity
States and propositions of a physical system
Quantum-mechanical features in terms of the logic of the physical system
On the hidden-variable issue
Proposition-state structure and idealized measurements
Superpositions of states and closure spaces
Transition-probability spaces and quantum systems
On the convex-set approach
Introduction to a quantum logic
Reconstruction of Hilbert-Space Quantum Mechanics
The coordinatization problem
Use of real and quaternionic Hibert Spaces: a simple example
Dynamics
Composition of physical systems
Hidden-variable theories and Gleason's Theorem
Introduction to quantum probability theory
Appendices
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521168496
ISBN-10: 052116849X
Series: Encyclopedia of Mathematics and Its Applications
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 336
Published: 9th December 2010
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.39 x 15.6  x 1.78
Weight (kg): 0.47