A Second Course in Topos Quantum Theory pp 79-105 | Cite as

# Interpreting Self-Adjoint Operators as *q*-Functions

## 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

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*A First Course in Topos Quantum Theory*. Lecture Notes in Physics, vol. 868 (Springer, Heidelberg, 2013)Google Scholar