A Topos Perspective on the Kochen-Specker Theorem:
III. Von Neumann Algebras as the Base Category
Hamilton, John and Isham, Chris and Butterfield, Jeremy (2000) A Topos Perspective on the Kochen-Specker Theorem:
III. Von Neumann Algebras as the Base Category.
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Abstract
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).
| Keywords: | Kochen-Specker theorem; von Neumann algebras; topos theory; interval-valuations; subobjects |
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| Subjects: | Specific Sciences: Physics: Quantum Mechanics |
| ID Code: | 1918 |
| Deposited By: | Butterfield, Jeremy |
| Deposited On: | 29 August 2004 |
| Additional Information: | Published in: International Journal of Theoretical Physics, volume 39, 2000, pages 1413-1436 |
| Alternative Locations: | http://arxiv.org/quant-ph/9911020 |