JournalsjncgVol. 7, No. 4pp. 939–979

Spectral geometry of the Moyal plane with harmonic propagation

  • Raimar Wulkenhaar

    University of Münster, Germany
  • Victor Gayral

    Université de Reims, France
Spectral geometry of the Moyal plane with harmonic propagation cover
Download PDF

Abstract

We construct a ‘non-unital spectral triple of finite volume’ out of the Moyal product and a differential square root of the harmonic oscillator Hamiltonian. We find that the spectral dimension of this triple is dd but the KO-dimension is 2d2d. We add another Connes–Lott copy and compute the spectral action of the corresponding Yang–Mills–Higgs model. As result, the ‘covariant coordinate’ involving the gauge field combines with the Higgs field to a unified potential, yielding a deep unification of discrete and continuous parts of the geometry.

Cite this article

Raimar Wulkenhaar, Victor Gayral, Spectral geometry of the Moyal plane with harmonic propagation. J. Noncommut. Geom. 7 (2013), no. 4, pp. 939–979

DOI 10.4171/JNCG/140