UID:
almahu_9947367804802882
Format:
1 online resource (821 p.)
Edition:
1st ed.
ISBN:
1-281-02923-8
,
9786611029234
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0-08-055038-X
Content:
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 struct
Note:
Description based upon print version of record.
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Front Cover; Handbook of Quantum Logic and Quantum Structures; Copyright Page; Table of Contents; Foreword; Editorial Preface; List of Authors; Chapter 1 New Quantum Structures; 1 INTRODUCTION; 2 QUANTUM LOGICS, EFFECT ALGEBRAS AND D-POSETS; 3 PSEUDO MV-ALGEBRAS; 4 PSEUDO EFFECT ALGEBRAS; 5 CONCLUSION; ACKNOWLEDGEMENTS; BIBLIOGRAPHY; Chapter 2 Quantum Structures and Fuzzy Set Theory; 1 INTRODUCTION; 2 BASIC NOTIONS AND DEFINITIONS; 3 MACZYNSKI'S FUNCTIONAL MODEL OF B-VN QUANTUM LOGIC; 4 THE GENERAL FUZZY SET MODEL OF B-VN QUANTUM LOGIC; 5 TWO PAIRS OF BINARY OPERATIONS
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6 GENERAL QUANTUM STRUCTURES AND FUZZY SETS7 EFFECT ALGEBRAS OF FUZZY SETS GENERATED BY NILPOTENT TRIANGULAR NORMS; 8 FUZZY SET MODELS OF QUANTUM PROBABILITY; 9 SUMMARY; ACKNOWLEDGMENTS; BIBLIOGRAPHY; Chapter 3 Algebraic and Measure-theoretic Properties of Classes of Subspaces of an Inner Product Space; 1 INTRODUCTION; 2 FAMILIES OF CLOSED SUBSPACES OF AN INNER PRODUCT SPACE S; 3 ALGEBRAIC STRUCTURE OF P(S), C(S), E(S), Eq(S), F(S) AND W(S); 4 ALGEBRAIC COMPLETENESS CRITERIA OF INNER PRODUCT SPACES; 5 MEASURES ON P(S), C(S), E(S), Eq(S), F(S) AND W(S)
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6 GLEASON AND DOROFEEV-SHERSTNEV THEOREMS7 IS EVERY REGULAR CHARGE ON L(H) COMPLETELY-ADDITIVE?; 8 MEASURE-THEORETIC COMPLETENESS CRITERIA OF INNER PRODUCT SPACES; 9 CONVERGENCE OF CHARGES; 10 INFINITE-VALUED MEASURES; ACKNOWLEDGEMENTS; BIBLIOGRAPHY; Chapter 4 Quantum Probability; 1 INTRODUCTION; 2 MOTIVATIONAL CALCULATIONS; 3 NOTATION AND DEFINITIONS; 4 PROBABILITY AND CONDITIONAL PROBABILITY; 5 INDEPENDENCE; 6 PROPERTIES OF THE SEQUENTIAL PRODUCT; 7 ALMOST SHARP EFFECTS; 8 NON-DISTURBANCE FOR FUZZY QUANTUM MEASUREMENTS; 9 SEQUENTIAL EFFECT ALGEBRAS; BIBLIOGRAPHY
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Chapter 5 Quantum Logics as Underlying Structures of Generalized Probability Theory1 INTRODUCTION; 2 BASIC DEFINITIONS AND FACTS; 3 COMPATIBLE SUBSETS OF A LOGIC; 4 STATES ON A LOGIC; 5 OBSERVABLES ON A LOGIC; 6 PARTIAL COMPATIBILITY AND JOINT DISTRIBUTIONS OF OBSERVABLES; 7 THE LOGIC OF CLOSED SUBSPACES OF A HILBERT SPACE; 8 JOINT DISTRIBUTIONS ON THE HILBERT SPACE LOGIC; 9 APPENDIX 1: UNCERTAINTY RELATIONS; 10 APPENDIX 2: BELL INEQUALITIES ON QUANTUM LOGICS; 11 QUANTUM LOGICS AND PHYSICAL SYSTEMS; 12 BELL INEQUALITIES; BIBLIOGRAPHY
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Chapter 6 Quantum Logic and Partially Ordered Abelian Groups1 INTRODUCTION; 2 ORTHODOX QUANTUM MECHANICS; 3 PROJECTIONS AND COMPRESSIONS; 4 SYMMETRIES; 5 MIXED STATES AND DENSITY OPERATORS; 6 EFFECT OPERATORS AND POV-MEASURES; 7 ABSTRACTION FROM P(h) AND E(h)-EFFECT ALGEBRAS; 8 CLASSIFICATION OF EFFECT ALGEBRAS; 9 PARTIALLY ORDERED ABELIAN GROUPS; 10 UNIVERSAL GROUPS; 11 ABSTRACTION FROM G(h)-UNITAL GROUPS; 12 SEMISIMPLICIAL UNITAL GROUPS; 13 INTERPOLATION UNIGROUPS AND THEIR UNIT INTERVALS; 14 UNITAL GROUPS OF REAL-VALUED FUNCTIONS; 15 EFFECT-ORDERED RINGS; 16 ABSTRACTION FROM P(h)-CB-GROUPS
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17 THE RICKART PROJECTION PROPERTY AND RC-GROUPS
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English
Additional Edition:
ISBN 0-444-52870-9
Language:
English
