New Trends in Quantum Structures by Anatolij DvurecenskijNew Trends in Quantum Structures by Anatolij Dvurecenskij

New Trends in Quantum Structures

byAnatolij Dvurecenskij, Sylvia Pulmannov

Paperback | December 15, 2010

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This monograph deals with the latest results concerning different types of quantum structures. This is an interdisciplinary realm joining mathematics, logic and fuzzy reasoning with mathematical foundations of quantum mechanics, and the book covers many applications. The book consists of seven chapters. The first four chapters are devoted to difference posets and effect algebras; MV-algebras and quantum MV-algebras, and their quotients; and to tensor product of difference posets. Chapters 5 and 6 discuss BCK-algebras with their applications. Chapter 7 addresses Loomis-Sikorski-type theorems for MV-algebras and BCK-algebras. Throughout the book, important facts and concepts are illustrated by exercises. Audience: This book will be of interest to mathematicians, physicists, logicians, philosophers, quantum computer experts, and students interested in mathematical foundations of quantum mechanics as well as in non-commutative measure theory, orthomodular lattices, MV-algebras, effect algebras, Hilbert space quantum mechanics, and fuzzy set theory.
Title:New Trends in Quantum StructuresFormat:PaperbackDimensions:542 pages, 23.5 × 15.5 × 0.01 inPublished:December 15, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048155258

ISBN - 13:9789048155255


Table of Contents

Preface. Introduction. 1. D-posets and Effect Algebras. 2. MV-algebras and QMV-algebras. 3. Quotients of Partial Abelian Monoids. 4. Tensor Product of D-Posets and Effect Algebras. 5. BCK-algebras. 6. BCK-algebras in Applications. 7. Loomis-Sikorski Theorems for MV-algebras and BCK-algebras. Bibliography. Index of Symbols. Index. List of Figures and Tables.

Editorial Reviews

` ...impressive monograph...presents some of the newest trends in the mathematical theory of structures arising in quantum mechanics. The book is well written, with special attention paid to mathematical accuracy. The book will be useful for mathematicians, but also for physicists and logicians, as well as for the reader interested in fuzzy set theory and quantum computing. Throughout the text important facts and concepts are illustrated by exercises.' Mathematical Reviews, 2002