Topos Perspective on the Kochen=nSpeckerTheorem: III. Von Neumann Algebras as theBase Category
- 96 Downloads
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.
KeywordsField Theory Real Number Elementary Particle Quantum Field Theory Quantum Theory
Unable to display preview. Download preview PDF.
- 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