Spectral geometry of the Moyal plane with harmonic propagation
Operator Algebras
2014-07-01 v1 High Energy Physics - Theory
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 d but the KO-dimension is 2d. We add another Connes-Lott copy and compute the spectral action of the corresponding U(1)-Yang-Mills-Higgs model. We find that 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.
Keywords
Cite
@article{arxiv.1108.2184,
title = {Spectral geometry of the Moyal plane with harmonic propagation},
author = {Victor Gayral and Raimar Wulkenhaar},
journal= {arXiv preprint arXiv:1108.2184},
year = {2014}
}
Comments
37 pages