Classification of finite spectral triples
Dec, 199629 pages
Published in:
- J.Geom.Phys. 28 (1998) 1-30
e-Print:
- hep-th/9701081 [hep-th]
Report number:
- CPT-96-P-3409
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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.Note:
- 29 pages, Latex, 2 figures Report-no: CPT-96/P.3409
- space-time
- gauge field theory: Yang-Mills
- differential forms
- differential geometry: noncommutative
- fermion
- operator: algebra
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