Noncommutative geometry, Lorentzian structures and causality

Nicolas Franco, Michał Eckstein

    Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)


    The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However, noncommutative geometry has mainly been developed using the Euclidean signature, and the typical Lorentzian aspects of space-time, the causal structure in particular, are not taken into account. We present an extension of noncommutative geometry \`a la Connes suitable the for accommodation of Lorentzian structures. In this context, we show that it is possible to recover the notion of causality from purely algebraic data. We explore the causal structure of a simple toy model based on an almost commutative geometry and we show that the coupling between the space-time and an internal noncommutative space establishes a new `speed of light constraint'.
    Original languageFrench
    Title of host publicationMathematical Structures of the Universe
    Place of PublicationKrakow
    PublisherMichał Heller, Michał Eckstein, Sebastian Szybka
    EditionCopernicus Center Press
    ISBN (Print)978-83-7886-107-2
    Publication statusPublished - 11 Sep 2014

    Cite this

    Franco, N., & Eckstein, M. (2014). Noncommutative geometry, Lorentzian structures and causality. In Mathematical Structures of the Universe (Copernicus Center Press ed., pp. 315-340). Michał Heller, Michał Eckstein, Sebastian Szybka.