A topos foundation for theories of physics: III. The representation of physical quantities with arrows δ̆o(A):Σ̱→R≽̱

DOI10.1063/1.2883777zbMath1152.81410arXivquant-ph/0703064OpenAlexW2112715110MaRDI QIDQ5504928

Andreas Döring, Chris J. Isham

Publication date: 23 January 2009

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0703064

Mathematics Subject Classification ID

General and philosophical questions in quantum theory (81P05) Topoi (18B25) Other applications of logic (03B80)

Related Items (20)

Topos models for physics and topos theory ⋮ Topos quantum theory on quantization-induced sheaves ⋮ Topos quantum theory reduced by context-selection functors ⋮ Gleason’s theorem for composite systems ⋮ A comparison of two topos-theoretic approaches to quantum theory ⋮ Spectral presheaves as quantum state spaces ⋮ Quantum entanglement: an analysis via the orthogonality relation ⋮ Contextuality and noncommutative geometry in quantum mechanics ⋮ Group action in topos quantum physics ⋮ Topologies on quantum topoi induced by quantization ⋮ Self-adjoint operators as functions. I: Lattices, Galois connections, and the spectral order ⋮ Intuitionistic quantum logic of an \(n\)-level system ⋮ Topos Quantum Logic and Mixed States ⋮ Negations and meets in topos quantum theory ⋮ A topos for algebraic quantum theory ⋮ A topos formulation of history quantum theory ⋮ A topos foundation for theories of physics: I. Formal languages for physics ⋮ A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory ⋮ A topos foundation for theories of physics: IV. Categories of systems ⋮ Classical and quantum probabilities as truth values

Cites Work

• Topos perspective on the Kochen-Specker theorem. I: Quantum states as generalized valuations
• Topos perspective on the Kochen-Specker theorem. III: Von Neumann algebras as the base category.
• Topos perspective on the Kochen--Specker theorem. IV: Interval valuations
• A topos perspective on the Kochen-Specker theorem. II: Conceptual aspects and classical analogues
• Kochen-Specker theorem for von Neumann algebras
• A topos foundation for theories of physics: I. Formal languages for physics
• A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory
• A topos foundation for theories of physics: IV. Categories of systems

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