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Abstract: In this fourth of our series of papers on observables we show that one canassociate to each von Neumann algebra R a pair of isomorphic presheaves, theupper presheaf O^{+} {R} and the lower presheaf O^{-} {R}, on the category ofabelian von Neumann subalgebras of R. Each $A \in R {sa}$ induces a globalsection of O^{+} {R} and of O^{-} {R} respectively. We call them \emph{contextual observables}. But we show that, in general, not every globalsection of these presheaves arises in this way. Moreover, we discuss states ofa von Neumann algebra in the presheaf context.

Author: Hans F. de Groote

Source: https://arxiv.org/

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