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Open Quantum Systems Decoherence
Observables IV: The presheaf perspective
arXiv
Authors: Hans F. de Groote
Year
2007
Paper ID
49460
Status
Preprint
Abstract Read
~2 min
Abstract Words
103
Citations
N/A
Abstract
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^{+}_{R} and the lower presheaf O^{-}_{R}, on the category of abelian von Neumann subalgebras of R. Each A in Rsa induces a global section of O^{+}_{R} and of O^{-}_{R} respectively. We call them \emph {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.
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- 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^+_R and...
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