Handbook of quantum logic and quantum structures : quantum structures / edited by Kurt Engesser, Dov M. Gabbay, Daniel Lehmann.

Format:

Book

Contributor:

Engesser, Kurt.

Gabbay, Dov M., 1945-

Lehmann, Daniel, 1946-

Emma Louise McClellan Fund.

Language:

English

Subjects (All):

Quantum logic.

Quantum theory.

Physical Description:

xvi, 801 pages : illustrations ; 25 cm

Place of Publication:

Amsterdam ; Boston : Elsevier, 2007.

Summary:

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics" quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate.

The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras, MV-algebras, partially ordered Abelian groups and those structures underlying quantum probability.

Contents:

New Quantum Structures / Anatolij Dvurecenskij 1

Quantum Structures and Fuzzy Set Theory / Jaroslaw Pykacz 55

Algebraic and Measure-theoretic Properties of Classes of Subspaces of an Inner Product Space / David Buhagiar, Emmanuel Chetcuti, Anatolij Dvurecenskij 75

Quantum Probability / Stan Gudder 121

Quantum Logics as Underlying Structures of Generalized Probability Theory / Pavel Ptak, Sylvia Pulmannova 147

Quantum Logic and Partially Ordered Abelian Groups / David J. Foulis, Richard J. Greechie 215

Quantum Structures and Operator Algebras / Jan Hamhalter 285

Constructions of Quantum Structures / Mirko Navara 335

D-Posets / Ferdinand Chovanec, Frantisek Kopka 367

Wigner's Theorem and its Generalizations / Georges Chevalier 429

Propositional Systems, Hilbert Lattices and Generalized Hilbert Spaces / Isar Stubbe, Bart Van Steirteghem 477

Equations and Hilbert Lattices / Rene Mayet 525

The Source of the Orthomodular Law / John Harding 555

Starting from the Convex Set of States / Enrico Beltrametti 587

Quantum Logic and Automata Theory / Mingsheng Ying 619

Quantum Logic and Quantum Computation / Mladen Pavicic, Norman D. Megill 755.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Emma Louise McClellan Fund.

ISBN:

9780444528704

0444528709

OCLC:

145554957