Ebook: Current Research in Operational Quantum Logic: Algebras, Categories, Languages

The present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati­ cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic.

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This edited volume gives an overview of the concepts and methods used in current research in quantum logic, viewed both as an operational physical theory and in terms of purely mathematical structure. Far from being simply a collation of research papers, it consists of 11 specially commissioned essays that, taken together, provide both an introduction to quantum logic and an overview of current research in this subject. The contributors, who include some of the most distinguished names in the field, discuss topics ranging from the algebraic theory of orthomodular lattices to recent applications of category-theoretic methods and connections with theoretical computer science. Moreover, an historical overview of the field and an extensive citation and concept index are included.
Audience: This volume, dedicated to D.J. Foulis in honour of his seminal contributions to quantum logic, should interest pure mathematicians, theoretical physicists, computer scientists and philosophers of science.

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This edited volume gives an overview of the concepts and methods used in current research in quantum logic, viewed both as an operational physical theory and in terms of purely mathematical structure. Far from being simply a collation of research papers, it consists of 11 specially commissioned essays that, taken together, provide both an introduction to quantum logic and an overview of current research in this subject. The contributors, who include some of the most distinguished names in the field, discuss topics ranging from the algebraic theory of orthomodular lattices to recent applications of category-theoretic methods and connections with theoretical computer science. Moreover, an historical overview of the field and an extensive citation and concept index are included.
Audience: This volume, dedicated to D.J. Foulis in honour of his seminal contributions to quantum logic, should interest pure mathematicians, theoretical physicists, computer scientists and philosophers of science.
Content:
Front Matter....Pages I-VII
Operational Quantum Logic: An Overview....Pages 1-36
Algebraic Aspects of Orthomodular Lattices....Pages 37-65
Observables in the Logico-Algebraic Approach....Pages 67-80
Test Spaces and Orthoalgebras....Pages 81-114
Representations on Unigroups....Pages 115-138
Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics....Pages 139-165
Short Introduction to Enriched Categories....Pages 167-194
Operational Galois Adjunctions....Pages 195-218
Operational Axiomatics and Compound Systems....Pages 219-244
Quantales....Pages 245-262
Quantales and Observational Semantics....Pages 263-288
Quantum Languages....Pages 289-310
Back Matter....Pages 311-325

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This edited volume gives an overview of the concepts and methods used in current research in quantum logic, viewed both as an operational physical theory and in terms of purely mathematical structure. Far from being simply a collation of research papers, it consists of 11 specially commissioned essays that, taken together, provide both an introduction to quantum logic and an overview of current research in this subject. The contributors, who include some of the most distinguished names in the field, discuss topics ranging from the algebraic theory of orthomodular lattices to recent applications of category-theoretic methods and connections with theoretical computer science. Moreover, an historical overview of the field and an extensive citation and concept index are included.
Audience: This volume, dedicated to D.J. Foulis in honour of his seminal contributions to quantum logic, should interest pure mathematicians, theoretical physicists, computer scientists and philosophers of science.
Content:
Front Matter....Pages I-VII
Operational Quantum Logic: An Overview....Pages 1-36
Algebraic Aspects of Orthomodular Lattices....Pages 37-65
Observables in the Logico-Algebraic Approach....Pages 67-80
Test Spaces and Orthoalgebras....Pages 81-114
Representations on Unigroups....Pages 115-138
Free Extensions of Group Actions, Induced Representations, and the Foundations of Physics....Pages 139-165
Short Introduction to Enriched Categories....Pages 167-194
Operational Galois Adjunctions....Pages 195-218
Operational Axiomatics and Compound Systems....Pages 219-244
Quantales....Pages 245-262
Quantales and Observational Semantics....Pages 263-288
Quantum Languages....Pages 289-310
Back Matter....Pages 311-325
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