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A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation. (English) Zbl 0451.03026

MSC:
03G12 Quantum logic
03B60 Other nonclassical logic
06C15 Complemented lattices, orthocomplemented lattices and posets
06C20 Complemented modular lattices, continuous geometries
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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References:
[1] D. Aerts and I. Daubechies, ?A characterization of subsystems in physics?,Lett. Math. Phys. 3, (1979).
[2] D. Aerts and I. Daubechies, ?Physical Justification for using the tensor product to describe two quantum systems as one joint system?, submitted toHelv. Phys. Acta.
[3] C.Piron,Foundations of Quantum Physics, W.A. Benjamin Inc., Reading, Massachusetts, 1976. · Zbl 0333.46050
[4] D. Aerts and I. Daubechies, ?Structure-preserving maps of a quantum mechanical propositional system?, to be published inHelv. Phys. Acta.
[5] D. Aerts and I. Daubechies, ?A connection between propositional systems in Hilbert space and von Neumann algebras?, to be published inHelv. Phys. Acta.
[6] D. Aerts and C. Piron, ?The role of the modular pairs in the category of complete orthomodular lattice?,Lett. Math. Phys., this issue. · Zbl 0451.03024
[7] J.Dixmier,Les algèbres d’opérateurs dans l’espace Hilbertien, Gauthier-Villars, Paris, 1969. · Zbl 0175.43801
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