Quantum Logic in Algebraic Approach, Softcover reprint of hardcover 1st ed. 1998 Fundamental Theories of Physics Series, Vol. 91

This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.

1 Introduction.- 2 Observables and states in the Hilbert space formalism of quantum mechanics.- 3 Lattice theoretic notions.- 4 Hilbert lattice.- 5 Physical theory in semantic approach.- 6 Von Neumann lattices.- 7 The Birkhoff-von Neumann concept of quantum logic.- 8 Quantum conditional and quantum conditional probability.- 9 The problem of hidden variables.- 10 Violation of Bell’s inequality in quantum field theory.- 11 Independence in quantum logic approach.- 12 Reichenbach’s common cause principle and quantum field theory.- References.

This book is the first to present quantum logic in relation to von Neumann algebra theory. Based on developing quantum logic in terms of operator algebras, the book reconstructs and reevaluates the Birkhoff--von Neumann concept of quantum logic. It also covers recent results such as the violation of Bell's inequality in relativistic quantum field theory, the logical independence of von Neumann lattices and the status of the common cause principle in quantum field theory. Other topics treated include the theory of quantum conditional and statistical inference, an operator algebraic treatment of the hidden variable problem and the semantic approach to physical theories. Audience: This volume will be of interest to mathematicians, physicists, mathematical physicists and historians and philos