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Similarity-Projection structures: The Logical Geometry of Quantum Physics

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  • Daniel Lehmann
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    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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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp482.pdf
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    Bibliographic Info

    Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp482.

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    Length: 30 pages
    Date of creation: May 2008
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    Handle: RePEc:huj:dispap:dp482

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    1. Daniel Lehmann, 2007. "A Presentation of Quantum Logic Based on an and then Connective," Discussion Paper Series dp442, The Center for the Study of Rationality, 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.
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