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Quantum Measure Theory : Fundamental Theories of Physics - Jan Hamhalter

Quantum Measure Theory

Fundamental Theories of Physics

Hardcover Published: 31st October 2003
ISBN: 9781402017148
Number Of Pages: 410

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This book has grown out of my research interests in the theory of oper­ ator algebras, orthomodular structures and mathematical foundations of quantum theory. It is based on a series of lectures on measure theory on nonboolean operator structures which I prepared for Ph. D. students in Workshops on Measure Theory and Real Analysis in Italy (Gorizia 1999, Grado 2001) and which I have delivered at the conferences of the Interna­ tional Quantum Structures Association in Berlin 1996, Cesena 2001, and Vienna 2002. I have worked on these subjects in the framework of Prague's Semi­ nar on Mathematical Formalism of Quantum Theory founded by P. Ptak. Many results presented in the book were also obtained during my longer research stays abroad, in particular at the Department of Mathematics, Reading University, U. K. (1993) and at the Mathematical Institute of Er­ langen University, Germany (1996-1997, 2000 and 2003). Both the research activity and the work on the book was supported by a few international projects I participated in. I would like to acknowledge the support of European Community that supported my research stay in Reading University (Grant COST, Noncommutative Measure Theory and von Neumann Algebras, 1993). I am also very much grateful to the Alexan­ der von Humboldt Foundation, Bonn, for long-term support of my research and for awarding me the grants that enabled me work at Erlangen Uni­ versity in 1996-1997, 2000 and 2003.

Operator Algebras
Von Neumann Algebras
Jordan Algebras And Ordered Structures
Gleason Theorem
Reduction To Three-Dimensional Space
Regularity Of Frame Functions On R3
Boundedness Of Frame Functions
Historical Remarks And Comments
Completeness Criteria
Functiona1 Completeness Criteria
Algebraic Completeness Criteria
Measure Theoretic Completeness Criteria
Historical Remarks And Comments
Generalized Gleason Theorem
The Mackey-Gleason Problem
Reduction To Scalar Quasi-Functionals
Linear Extensions Of Measures On Type In Algebras
Linear Extensions Of Measures On Infinite Algebras
Linear Extensions Of Measures On Finite Algebras
Historical Remarks And Comments
Basic Principles Of Quantum Measure Theory
Boundedness Of Completely Additive Measures
Yosida-Hewitt Decompositions Of Quantum Measures
Convergence Theorems
Historical Remarks And Comments
Applications Of Gleason Theorem
Multiform Gleason Theorem And Decoherence
Velocity Maps And Derivations
Approximate Hidden Variables
Historical Remarks And Comments
Orthomorphisms Of Projections
Orthomorphisms Of Projection Lattices
Countable Additivity Of *-Homomorphisms
Historical Remarks And Comments
Restrictions And Extensions Of States
Restriction Properties Of Pure States
Gleason Type Theorems For Quantum Logics
Historical Remarks And Comments
Jauch-Piron States
Basic Properties Of Jauch States
Nonsingularity Of Jauch-Piron States
Countable Additivity Of States
Historical Remarks And Comments
Independence Of Quantum Systems
Independence In Classical And Quantum Theory
Independence Of C*-Algebras
Independence Of Von Neumann Algebras
Historical Remarks And Comments
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9781402017148
ISBN-10: 1402017146
Series: Fundamental Theories of Physics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 410
Published: 31st October 2003
Publisher: Springer-Verlag New York Inc.
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.77