Electrodynamics from noncommutative geometry

Koen Van Den Dungen, Walter D. Van Suijlekom

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    Within the framework of Connes' noncommutative geometry, the notion of an almost commutative manifold can be used to describe field theories on compact Riemannian spin manifolds. The most notable example is the derivation of the Standard Model of high energy physics from a suitably chosen almost commutative manifold. In contrast to such a non-abelian gauge theory, it has long been thought impossible to describe an abelian gauge theory within this framework. The purpose of this paper is to improve on this point. We provide a simple example of a commutative spectral triple based on the two-point space and show that it yields a U.1/-gauge theory. Then we slightly modify the spectral triple such that we obtain the full classical theory of electrodynamics on a curved background manifold.

    Original languageEnglish
    Pages (from-to)433-456
    Number of pages24
    JournalJournal of Noncommutative Geometry
    Volume7
    Issue number2
    DOIs
    Publication statusPublished - 2013

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