A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category

Hamilton, J.; Isham, C. J.; Butterfield, J.

A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category

Authors

Hamilton, J.

Isham, C. J.

Butterfield, J.

Description

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).
Latex2e