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Title: Contextuality and noncommutative geometry in quantum mechanics
Author: de Silva, Nadish
ISNI:       0000 0004 5354 4095
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a construction meant to analyze contextuality in quantum mechanics, to derive simple reconstructions of noncommutative topological tools from their topological prototypes is presented. We associate to each unital C*-algebra A a geometric object--a diagram of topological spaces representing quotient spaces of the noncommutative space underlying A—meant to serve the role of a generalized Gel'fand spectrum. After showing that any functor F from compact Hausdorff spaces to a suitable target category C can be applied directly to these geometric objects to automatically yield an extension F which acts on all unital C*-algebras, we compare a novel formulation of the operator K0 functor to the extension K of the topological K-functor. We then conjecture that the extension of the functor assigning a topological space its topological lattice assigns a unital C*-algebra the topological lattice of its primary ideal spectrum and prove the von Neumann algebraic analogue of this conjecture.
Supervisor: Abramsky, Samson; Coecke, Bob Sponsor: Clarendon Fund ; Natural Sciences and Engineering Research Council of Canada ; University of Oxford
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Analytic Topology or Topology ; Computer science (mathematics) ; Quantum theory (mathematics) ; Functional analysis (mathematics) ; Theoretical physics ; contextuality ; noncommutative geometry ; operator algebras ; k-theory ; quantum physics ; quantum mechanics ; functional analysis