Representations of Quantum Logics and Transition Probability Spaces

  • Sylvia Pulmannova
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


Two axiomatic approaches to quantum mechanics are compared : the quantum-logic approach and the transition-probabi1ity spaces approach. It is shown that the quantum-logic approach is more general than the transition-probability spaces approach. Necessary and sufficient conditions -for the equivalence of these approaches are found. As a generalization of the above approaches, a notion of an orthogonality space is introduced. Conditions under which an orthogonality space can be represented in a generalized Hilbert space are investigated.


Probability Space Characteristic Subset Quantum Logic Division Ring Hermitian Form 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Sylvia Pulmannova
    • 1
  1. 1.Mathematics InstituteSlovak Academy of SciencesBratislavaCzechoslovakia

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