Quantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations

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dc.creatorZafiris, Elias
dc.date2004-05-02
dc.date2007-03-14
dc.date.accessioned2026-07-07T10:48:15Z
dc.date.available2026-07-07T10:48:15Z
dc.descriptionWe construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local arithmetics in measurement situations. This construction makes possible the adaptation of the methodology of Abstract Differential Geometry (ADG), a la Mallios, in a topos-theoretic environment, and hence, the extension of the "mechanism of differentials" in the quantum regime. The process of gluing information, within diagrams of commutative algebraic localizations, generates dynamics, involving the transition from the classical to the quantum regime, formulated cohomologically in terms of a functorial quantum connection, and subsequently, detected via the associated curvature of that connection.
dc.description81 pages, replaced by expanded published version
dc.identifierhttps://arxiv.org/abs/gr-qc/0405009
dc.identifierhttp://arxiv.org/abs/gr-qc/0405009
dc.identifierInt.J.Theor.Phys.46:237-243,2007
dc.identifierdoi:10.1007/s10773-006-9231-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183811
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleQuantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations
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