Classification of Finite Spectral Triples

Details Classification of Finite Spectral Triples Classification of Finite Spectral Triples

1997-01-16

arxiv.org/abs/hep-th/9701081v2

J.Geom.Phys. 28 (1998) 1-30

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 29 pages with 2 figures, reference added

Scientific paper

10.1016/S0393-0440(97)00068-5

It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in terms of matrices and classified using diagrams. When tensorized with the ordinary space-time geometry, finite spectral triples give rise to Yang-Mills theories with spontaneous symmetry breaking, whose characteristic features are given within the diagrammatic approach: vertices of the diagram correspond to gauge multiplets of chiral fermions and links to Yukawa couplings.

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