Topos Perspective on the Kochen=nSpeckerTheorem: III. Von Neumann Algebras as theBase Category
Article
- 98 Downloads
- 35 Citations
Abstract
We extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as theKochen–Specker theorem. This extension has two main parts: the use of vonNeumann algebras as a base category and the relation of our generalized valuationsto (i) the assignment to quantities of intervals of real numbers and (ii) the ideaof a subobject of the coarse-graining presheaf.
Keywords
Field Theory Real Number Elementary Particle Quantum Field Theory Quantum Theory
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
REFERENCES
- 1.C. J. Isham and J. Butterfield (1998). A topos perspective on the Kochen-Specker theorem: I. Quantum states as generalised valuations. Int.J.Theor.Phys. 37, 2669–2733.Google Scholar
- 2.J. Butterfield and C. J. Isham (1999). A topos perspective on the Kochen-Specker theorem: II. Conceptual aspects, and classical analogues. Int.J.Theor.Phys. 38, 827–859.Google Scholar
- 3.S. Kochen and E. P. Specker (1967). The problem of hidden variables in quantum mechanics. J.Math.Mech. 17, 59–87.Google Scholar
- 4.R. Clifton. Beables in algebraic quantum theory. In From Physics to Philosophy, J. Butterfield and C. Pagonis, eds. (Cambridge University Press, Cambridge 1999), pp. 12–44.Google Scholar
- 5.H. Halvorson and R. Clifton (1999). Maximal beable subalgebras of quantum-mechanical observables, Int.J.Theor.Phys. 38, 2441–2484.Google Scholar
- 6.R. V. Kadison and J. R. Ringrose. Fundamentals of the Theory of Operator Algebras Volume1: Elementary Theory (Academic Press, New York, 1983).Google Scholar
- 7.C. Mulvey and J. W. Pelletier (1999). On the quantisation of points. J.Pure Appl.Algebra.Google Scholar
Copyright information
© Plenum Publishing Corporation 2000