Minimal supports in quantum logics and Hilbert space
type: Item
instance of: scholarly article
title: Minimal supports in quantum logics and Hilbert space
zbMATH Open document ID: 0642.03035
DOI: 10.1007/BF00668776
author: George Svetlichny
author: David Cohen
published in: International Journal of Theoretical Physics
publication date: 1987-01-01T00:00:00Z
review text: It is shown that if a fully atomic, complete orthomodular lattice satisfies a ``minimal support condition'' (m.s.c.), then it satisfies Piron's axioms, and is thereby shown to be the projection lattice of a generalized Hilbert space. It is shown, conversely, that m.s.c. holds in Hilbert space subspace lattices. The physical justification for m.s.c. is provided in the context of a property lattice \({\mathcal L}({\mathcal A},\Sigma)\) for a realistic entity (\({\mathcal A},\Sigma)\) in the sense of Foulis-Piron- Randall. This context provides a clear focus on key issues in the debate over the appropriateness of requiring quantum logics to be represented over Hilbert spaces.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 4045736
zbMATH Keywords: Hilbert space
zbMATH Keywords: physical entity
zbMATH Keywords: minimal support condition
zbMATH Keywords: Piron's axioms
zbMATH Keywords: projection lattice of a generalized Hilbert space
zbMATH Keywords: quantum logics
MaRDI profile type: Publication
cites work: Q4100556
cites work: Q4726887
description: scientific article; zbMATH DE number 4045736