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Brief Introduction to Covariant Topos Quantum Theory

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

Abstract

In this chapter we will describe a different way in which topos theory was utilised to describe quantum theory. This approach is called covariant topos quantum theory and it was first put forward in [42]. The aim of this approach is to combine, on the one hand, algebraic quantum theory by describing a system via a C-algebra \(\mathcal {A}\) and, on the other, Bohr’s idea of classical snapshots which enables one to talk about physical quantities, only with respect to a suitable context of compatible physical quantities.

References

  1. 5.
    B. Banaschewski, C.J. Mulvey, A globalisation of the Gelfand duality theorem. Ann. Pure Appl. Logic 137, 62–103 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 10.
    T. Coquand, B. Spitters, Integrals and valuations. J. Logic Anal. 1(3), 1–22 (2009)MathSciNetzbMATHGoogle Scholar
  3. 18.
    A. Doering, The physical interpretation of daseinisation. arXiv: 1004.3573 [quant-ph]Google Scholar
  4. 24.
    A. Doering, C. Isham, ‘What is a thing?’: Topos theory in the foundations of physics. arXiv:0803.0417 [quant-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
  6. 42.
    C. Heunen, N.P. Landsman, B. Spitters, A topos for algebraic quantum theory. Commun. Math. Phys. 291(1), 63–110 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 43.
    C. Heunen, N.P. Landsman, B. Spitters, S. Wolters, The Gelfand spectrum of a noncommutative C*-algebra: a topos-theoretic approach. J. Aust. Math. Soc. 90, 39 (2011). arXiv:1010.2050 [math-ph]Google Scholar
  8. 48.
    P.T. Johnstone, Open locales and exponentiation. Contemp. Math. 30, 84–116 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 50.
    P.T. Johnstone, Sketches of an Elephant A Topos Theory Compendium I, II (Oxford Science Publications, Oxford, 2002)zbMATHGoogle Scholar
  10. 74.
    S.A.M. Wolters, Quantum Toposophy UB Nijmegen [host] (2013)Google Scholar
  11. 75.
    S. Wolters, A comparison of two topos-theoretic approaches to quantum theory. arXiv:1010.2031 [math-ph]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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