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

1999/11/05 by J. Hamilton, John R. Hamilton, Hamilton, J. +5 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/9911020

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arxiv created 1999/11/05 · openalex publication_date 1999/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Cited by

• Complex Numbers, One-Parameter of Unitary Transformations and Stone's Theorem in Topos Quantum Theory
• Superlogic Manifolds and Geometric approach to Quantum Logic
• Group Action in Topos Quantum Physics
• Kochen–Specker Theorem for von Neumann Algebras
• Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Related

• A topos perspective on the Kochen-Specker theorem: II. Conceptual Aspects, and Classical Analogues:
• A topos perspective on the Kochen-Specker theorem: I. Quantum States as Generalized Valuations
• A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations
• A Comparison of Two Topos-Theoretic Approaches to Quantum Theory
• Topos-Theoretic Approaches to Quantum Theory