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Current Issues in Quantum Logic

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概要 These are the proceedings of the Workshop on Quantum Logic held in Erice (Sicily), December 2 - 9, 1979, at the Ettore Hajorana Centre for Scientific Culture. A conference of this sort was originally ...proposed by Giuliano Toraldo di Francia, who suggested the idea to Antonino Zichichi, and thus laid the foundation for the Workshop. To both of them we express our appreciation and thanks, also on behalf of the other participants, for having made this conference possible. There were approximately fifty participants; their names and institutions are listed in the text. Quantum logic, which has now a history of some forty or more years, has seen remarkable growth during the sixties and seventies. The papers in the present volume presuppose, by and large, some acquaintance with the elements of the subject. These may be found in the well-known books by J.H. Jauch (Foundations of Quantum Hechanics; Reading, 1968), V.S. Varadarajan (Geometry of Quantum Theory: Princeton, 1968), and C. Piron (Foundations of Quantum Theory; New York, 1976). The initial program for the conference listed about twenty-five invited papers. But in the context of a very active and qualified attendance, other contributions were offered. This volume contains all of them. The program listed six main topics: I. Classification or different areas of quantum logic, and open problems. II. Comparison and unification of different approaches to quantum theories; problems of interpretation. III. Formal quantum logic; axiomatics. IV. Hodal interpretations of quantum logic. v vi FOREWORD V. Quantum set theory.続きを見る
目次 1: Classification of Different Areas of Quantum Logic, and Open Problems
Classification of different areas of work afferent to quantum logic
Assumptions and interpretations of quantum logic
2: Comparison and Unification of Different Approaches to Quantum Theories; Problems of Interpretation
What are quantum logics and what ought they to be?
Charting the labyrinth of quantum logics: a progress report
Realism and quantum logic
What does quantum logic explain?
A new approach to equivalence in quantum logic
How to rewrite a stochastic dynamical theory so as to generate a measurement paradox
The quantum logical and the operational description for physical systems
3: Formal Quantum Logic; Axiomatics
Partial referential matrices for quantum logics
Some metalogical pathologies of quantum logic
Quantum logic as an extension of classical logic
Sequential quantum logic
Entailment and Quantum Logic
Some problems and methods in formal quantum logic
4: Modal Interpretations of Quantum Logic
A modal interpretation of quantum mechanics
The dialogic approach to modalities in the language of quantum physics
The inner language of operational quantum mechanics
5: Quantum Set Theory
Quantum set theory
Quantum sets, assemblies and plexi
Omologic as a Hilbert type calculus
Measure and integration in quantum set theory
6: Advances Concerning Mathematical Structure; Other Problems
Commutativity and generalized transition probability in quantum logic
Representations of Baer *-semigroups and quantum logics in Hilbert space
A non-standard quantum logic with a strong set of states
Description of compound physical systems and logical interaction of physical systems
Products of logics
Space time structure from quantum logic
Causal logic of Minkowski space-time
Propositional systems in field theories and lattice-valued quantum logics
Non-linear integration and signed measures on von Neumann algebras
On the inter-relations of the three quantal principles
On the non-unique decomposability of quantum mixtures
Motion and form
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Author Index.
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登録日 2020.06.27
更新日 2020.06.28