# A Topos for Algebraic Quantum Theory

@article{Heunen2009ATF,
title={A Topos for Algebraic Quantum Theory},
author={C. Heunen and N. P. Landsman and Bas Spitters},
journal={Communications in Mathematical Physics},
year={2009},
volume={291},
pages={63-110}
}
• Published 2009
• Physics, Mathematics
• Communications in Mathematical Physics
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos $${\mathcal{T}(A)}$$ in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra {\underline{A… Expand
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It is proved that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” of A, which is a commutative Rickart C*-algebra in the topos of functors from A to the category of sets. Expand
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