Handbook of Quantum Logic and Quantum Structures: Quantum Structures
Kurt Engesser, Dov M. Gabbay, Daniel Lehmann
Elsevier, Aug 11, 2011 - Computers - 818 pages
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.
- Written by eminent scholars in the field of logic
- A comprehensive presentation of the theory, approaches and results in the field of quantum logic
- Volume focuses on quantum structures
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Chapter 4 Quantum Probability
Chapter 5 Quantum Logics as Underlying Structures of Generalized Probability Theory
Chapter 6 Quantum Logic and Partially Ordered Abelian Groups
Chapter 9 DPosets
Chapter 10 Wigners Theorem and its Generalizations
Chapter 11 Propositional Systems Hilbert Lattices and Generalized Hilbert Spaces
Chapter 12 Equations and Hilbert Lattices
Chapter 13 The Source of the Orthomodular Law
Chapter 14 Starting from the Convex Set of States
Chapter 15 Quantum Logic and Automata Theory
Chapter 16 Quantum Logic and Quantum Computation
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a s b a,b e atoms automata automaton automorphism Beltrametti bijection binary Boolean algebra bounded C*-algebra called Chetcuti classical closed subspaces commutative compatible convex COROLLARY countable decomposition defined DEFINITION denote Dvurečenskij elements equations equivalent example exists Foulis function fuzzy sets Gleason's theorem Greechie diagram Gudder Hamhalter hence Hilbert lattice Hilbert space homomorphism implies inner product space isomorphic Kalmbach Lemma linear mapping Math mathematical Mayet morphism MV-algebra Navara Neumann algebra notion observables operator orthoalgebra orthogonal orthomodular lattice orthomodular lattice-valued orthomodular poset pairwise partially ordered Phys poset probability measure projection lattice projective geometry Proof prove pseudo effect algebra pseudo MV-algebra Pták Pulmannová quantum logic quantum mechanics quantum structures recş result satisfies self-adjoint sequence subalgebra sublogic subset theory unigroup unique unital group valued von Neumann algebra Wigner's theorem
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