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- Aerts, D. and Daubechies, I. (1979). A connection between propositional systems in Hilbert spaces and Von Neumann algebra's.
Helvetica Physica Acta,52,pp. 184-199. doi: 10.5169/seals-115025. download pdf.

Abstract:A theorem of Bade proves that for a complete Boolean sublattice of a Hilbert space lattice the sublattice is equal to the set of projections in its Von Neumann algebra. We prove that this theorem does not hold for the physically interesting class of non-Boolean propositional systems embedded in a Hilbert space lattice; we derive however a necessary and sufficient condition under which the theorem does hold. This condition is automatically satisfied if the propositional system is Boolean.- Aerts, D. and Daubechies, I. (1979). Characterization of subsystems in physics.
Letters in Mathematical Physics,3,pp. 11-17. doi: 10.1007/BF00959533, download pdf.

Abstract:Working within the framework of the propositional system formalism, we use a previous study of the description of two independent physical systems as one big physical system to derive a characterization of a (non-interacting) physical subsystem. We discuss the classical case and the quantum case.- Aerts, D. and Daubechies, I. (1979). Mathematical condition for a sub-lattice of a propositional system to represent a physical subsystem with a physical interpretation.
Letters in Mathematical Physics,3,pp. 19-27. download pdf

Abstract:We display three equivalent conditions for a sublattice, isomorphic to a P(H), of the propositional system P(H) of a quantum system to be the representation of a physical subsystem. These conditions are valid for dim H > 2. We prove that one of them is still necessary and sufficient if dim H < 3. A physical interpretation of this condition is given.- Aerts, D. and Piron, C. (1979). The role of modular pairs in the category of complete orthomodular lattices.
Letters in Mathematical Physics,3,pp. 1-10. doi: 10.1007/BF00959532. download pdf.

Abstract:We study the modular pairs of a complete orthomodular lattice i.e. a CROC. We propose the concept of m-morphism as a mapping which preserves the lattice structure, the orthogonality and the property to be a modular pair. We give a characterization of the m-morphisms in the case of the complex Hilbert space to justify this concept.

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1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,