International Journal of Theoretical Physics

, Volume 48, Issue 1, pp 261–281 | Cite as

Similarity-Projection Structures: The Logical Geometry of Quantum Physics

  • Daniel Lehmann


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.


Similarity-Projection structures Measurement algebras Quantum Logic 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Engineering and Center for the Study of RationalityHebrew UniversityJerusalemIsrael

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