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arXiv · hep-th/9701081

Classification of Finite Spectral Triples

Thomas Krajewski
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Abstract

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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Thomas Krajewski. 1997-01-20. Classification of Finite Spectral Triples. https://doi.org/10.1016/s0393-0440(97)00068-5

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