Abstract
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical Boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.
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References
Lehmann, D.: A presentation of quantum logic based on an “and then” connective. J. Log. Comput. 18(1), 59–76 (2008). doi:10.1093/logcom/exm054
Lehmann, D.: Quantic superpositions and the geometry of complex Hilbert spaces. Int. J. Theor. Phys. 47(5), 1333–1353 (2008). doi:10.1007/s10773-007-9576-y
Lehmann, D., Engesser, K., Gabbay, D.M.: Algebras of measurements: the logical structure of quantum mechanics. Int. J. Theor. Phys. 45(4), 698–723 (2006). doi:10.1007/s10773-006-9062-y
Peres, A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1995)
Whitney, H.: On the abstract properties of linear dependence. Am. J. Math. 57, 509–533 (1935)
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This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence.
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Lehmann, D. Similarity-Projection Structures: The Logical Geometry of Quantum Physics. Int J Theor Phys 48, 261–281 (2009). https://doi.org/10.1007/s10773-008-9801-3
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DOI: https://doi.org/10.1007/s10773-008-9801-3