Use this URL to cite or link to this record in EThOS:  https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.658528 
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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Abstract:  
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 objecta 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 K_{0} functor to the extension K^{∼} of the topological Kfunctor. 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:  uk.bl.ethos.658528  DOI:  Not available  
Keywords:  Analytic Topology or Topology ; Computer science (mathematics) ; Quantum theory (mathematics) ; Functional analysis (mathematics) ; Theoretical physics ; contextuality ; noncommutative geometry ; operator algebras ; ktheory ; quantum physics ; quantum mechanics ; functional analysis  
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