Lorentzian approach to noncommutative geometry

    Student thesis: Doc typesDoctor of Sciences

    Abstract

    This thesis concerns the research on a Lorentzian generalization of Alain Connes’ noncommutative geometry. In the first chapter, we present an introduction to noncommutative geometry within the context of unification theories. The second chapter is dedicated to the basic elements of noncommutative geometry as the noncommutative integral, the Riemannian distance function and spectral triples. In the last chapter, we investigate the problem of the generalization to Lorentzian manifolds. We present a first step of generalization of the distance function with the use of a global timelike eikonal condition. Then we set the first axioms of a temporal Lorentzian spectral triple as a generalization of a pseudo-Riemannian spectral triple together with a notion of global time in noncommutative geometry.
    Date of Award31 Aug 2011
    Original languageEnglish
    Awarding Institution
    • University of Namur
    SupervisorDOMINIQUE LAMBERT (Supervisor), Anne LEMAITRE (Supervisor), Andre Fuzfa (Jury), Timoteo Carletti (President), Pierre MARTINETTI (Jury) & Marc LACHIEZE-REY (Jury)

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