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Similarity-Projection structures: The Logical Geometry of Quantum Physics

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  • Daniel Lehmann

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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  • Daniel Lehmann, 2008. "Similarity-Projection structures: The Logical Geometry of Quantum Physics," Discussion Paper Series dp482, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp482
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    References listed on IDEAS

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    1. Daniel Lehmann, 2007. "Quantic Superpositions and the Geometry of Complex Hilbert Spaces," Discussion Paper Series dp447, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Daniel Lehmann, 2007. "A Presentation of Quantum Logic Based on an and then Connective," Levine's Bibliography 321307000000000735, UCLA Department of Economics.
    3. Daniel Lehmann, 2007. "A Presentation of Quantum Logic Based on an and then Connective," Discussion Paper Series dp442, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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