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


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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[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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