Coherent quantum logic
type: Item
instance of: scholarly article
title: Coherent quantum logic
zbMATH Open document ID: 0618.03034
DOI: 10.1007/BF00669595
published in: International Journal of Theoretical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author, unsatisfied with the von Neumann quantum logic, pursues the structural parallel between set algebra and linear algebra of Grassmann and Peano. Along these lines he compares three types of quantum logic: (1) the lattic logic of von Neumann, (2) a Clifford algebraic logic, and (3) a Grassmann algebraic logic. The last quantum logic is recommended as the most plausible one because of the following reasons: (1) It is highly symmetric; (2) the unimodular groups of the Peano algebras include the time-space structural group, which is now to be regarded as the unimodular group SL(2,\({\mathbb{C}})\) of two-component spinors, or its higher dimensional analogues SL(N,\({\mathbb{C}})\); (3) the isomorphism of the algebras of classes and sets seems to resolve basic conceptual problems of time-space structure.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 4002095
zbMATH Keywords: quantum logic
zbMATH Keywords: Clifford algebra
zbMATH Keywords: Grassmann algebra
zbMATH Keywords: unimodular groups
zbMATH Keywords: Peano algebras
author: David R. Finkelstein
reviewed by: Hirokazu Nishimura
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4002095