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Interpreting Self-Adjoint Operators as q-Functions

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

Abstract

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.

References

  1. 8.
    H. Comman, Upper regularization for extended self-adjoint operators. J. Oper. Theory 55(1), 91–116 (2006)MathSciNetzbMATHGoogle Scholar
  2. 12.
    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

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

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

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