Quantum Measure Theory Fundamental Theories of Physics
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Paperback. 412 pages. Dimensions: 9.2in. x 6.1in. x 0.9in.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 Pragues 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9789048164653
About this title:
This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.
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