Interpreting Self-Adjoint Operators as q-Functions

  • Cecilia Flori
Part of the Lecture Notes in Physics book series (LNP, volume 944)


In [20, 21] the authors show how it is possible to interpret self-adjoint operators affiliated with a von Neumann algebra \(\mathcal {N}\), as real-valued functions on the projection lattice \(P(\mathcal {N})\) of the algebra. These functions are called q-observable functions . The method of utilising real-valued function on \(P(\mathcal {N})\) to define self-adjoint operators was first introduced in [12] and, independently, in [8]. However, the novelty of the approach defined [20, 21] consists in the fact that these real valued functions are related to both the daseinisation map, central to topos quantum theory, and to quantum probabilities.


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    H. Comman, Upper regularization for extended self-adjoint operators. J. Oper. Theory 55(1), 91–116 (2006)MathSciNetzbMATHGoogle Scholar
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    H.F. de Groote, Observables IV: the presheaf perspective (2007). arXiv:0708.0677 [math-ph]Google Scholar
  3. 20.
    A. Doering, B. Dewitt, Self-adjoint operators as functions I: lattices, Galois connections, and the spectral order (2012). arXiv:1208.4724 [math-ph]Google Scholar
  4. 21.
    A. Doering, B. Dewitt, Self-adjoint operators as functions II: quantum probability. arXiv:1210.5747 [math-ph]Google Scholar
  5. 26.
    C. Flori, A First Course in Topos Quantum Theory. Lecture Notes in Physics, vol. 868 (Springer, Heidelberg, 2013)Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  • Cecilia Flori
    • 1
  1. 1.Computing and Mathematical SciencesThe Waikato UniversityHamiltonNew Zealand

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