Similarity-Projection structures: the logical geometry of Quantum Physics

Details Similarity-Projection structures: the logical geometry of Quantum Physics Similarity-Projection structures: the logical geometry of Quantum Physics

2008-05-06

arxiv.org/abs/0805.0726v1

Physics

Quantum Physics

29 pages

Scientific paper

10.1007/s10773-008-9801-3

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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