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

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

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

Quantum Physics 2007-05-23 v1

Authors: J. Hamilton , C. J. Isham , J. Butterfield

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

topos theory kochen-specker theorem von neumann algebras quantum valuations coarse-graining presheaf

Cite

@article{arxiv.quant-ph/9911020,
  title  = {A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category},
  author = {J. Hamilton and C. J. Isham and J. Butterfield},
  journal= {arXiv preprint arXiv:quant-ph/9911020},
  year   = {2007}
}

Comments

Latex2e

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

Abstract

Keywords

Cite

Comments

Related papers