caa a22 4500 463197585 CHVBK 20180406164927.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s10773-006-9223-z doi (NATIONALLICENCE)springer-10.1007/s10773-006-9223-z Zafiris Elias Institute of Mathematics, University of Athens, Panepistimioupolis, 15784, Athens, Greece aut Quantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations [Elektronische Daten] [Elias Zafiris] We 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), à 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. Springer Science + Business Media, Inc., 2006 quantum observables nationallicence commutative algebras nationallicence sheaves nationallicence topos theory nationallicence grothendieck topology nationallicence adjunction nationallicence adjoint functors nationallicence cohomology of algebras nationallicence connection nationallicence curvature nationallicence quantum dynamics nationallicence differential geometry nationallicence International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/2(2007-02-01), 319-382 0020-7748 46:2<319 2007 46 10773 https://doi.org/10.1007/s10773-006-9223-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9223-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Zafiris Elias Institute of Mathematics, University of Athens, Panepistimioupolis, 15784, Athens, Greece aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/2(2007-02-01), 319-382 0020-7748 46:2<319 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer