Current Research in Operational Quantum Logic

by Coecke, Bob; Moore, David; Wilce, Alexander

• ISBN13: 9780792362586
• ISBN10: 0792362586
• Format: Hardcover
• Copyright: 2000-03-01
• Publisher: Kluwer Academic Pub

Summary

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.

Table of Contents

Introduction Operational quantum logic: An overview	1	(36)
Bob Coecke
David Moore
Alexander Wilce
I. Algebras
Algebraic aspects of orthomodular lattices	37	(30)
Gunter Bruns
John Harding
Observables in the logico-algebraic approach	67	(14)
Pavel Ptak
Test spaces and orthoalgebras	81	(34)
Alexander Wilce
Representations on unigroups	115	(24)
David J. Foulis
Free extensions of group actions, induced representations, and the foundations of physics	139	(28)
David J. Foulis
Alexander Wilce
II. Categories
Short introduction to enriched categories	167	(28)
Francis Borceux
Isar Stubbe
Operational Galois adjunctions	195	(24)
Bob Coecke
David Moore
Operational axiomatics and compound systems	219	(26)
Frank Valckenborgh
Quantales	245	(18)
Jan Paseka
Jiri Rosicky
III. Languages
Quantales and observational semantics	263	(26)
Pedro Resende
Quantum languages	289	(28)
Stan Gudder
Indices
Concept index	311	(6)
Citation index	317