Observables IV : The Presheaf Perspective
نویسنده
چکیده
In this fourth of our series of papers on observables we show that one can associate to each von Neumann algebra R a pair of isomorphic presheaves, the upper presheaf O Rand the lower presheaf O − R , on the category of abelian von Neumann subalgebras of R. Each A ∈ Rsa induces a global section of O R and of O − R respectively. We call them contextual observables. But we show that, in general, not every global section of these presheaves arises in this way. Moreover, we discuss states of a von Neumann algebra in the presheaf context. ∗[email protected]; FB Mathematik, J.W.Goethe-Universität Frankfurt a. M. 1 ar X iv :0 70 8. 06 77 v1 [ m at hph ] 5 A ug 2 00 7
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