Moduli spaces of Dirac operators for finite spectral triples
arXiv:0902.2068 · doi:10.1007/978-3-8348-9831-9_2
Abstract
The structure theory of finite real spectral triples developed by Krajewski and by Paschke and Sitarz is generalised to allow for arbitrary KO-dimension and the failure of orientability and Poincare duality, and moduli spaces of Dirac operators for such spectral triples are defined and studied. This theory is then applied to recent work by Chamseddine and Connes towards deriving the finite spectral triple of the noncommutative-geometric Standard Model.
AMS-LaTeX, 60 pp. Revised version of qualifying year project (Master's thesis equivalent), BIGS, University of Bonn. V2: Final version with minor corrections, to appear in the Proceedings of the Workshop on Quantum Groups and Noncommutative Geometry, M. Marcolli and D. Parashar (eds.)
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Cited by in corpus (7)
- Early Universe models from Noncommutative Geometry
- A reconstruction theorem for almost-commutative spectral triples
- Clifford Algebras and Spinors
- Understanding truncated non-commutative geometries through computer simulations
- Coupling of gravity to matter, spectral action and cosmic topology
- Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
- On the finite spectral triple of an almost-commutative geometry