Ginsparg-Wilson relation, topological invariants and finite noncommutative geometry

@article{Aoki2003GinspargWilsonRT,
  title={Ginsparg-Wilson relation, topological invariants and finite noncommutative geometry},
  author={Hajime Aoki and Satoshi Iso and Keiichi Nagao},
  journal={Physical Review D},
  year={2003},
  volume={67},
  pages={085005}
}
We show that the Ginsparg-Wilson (GW) relation can play an important role to define chiral structures in {\it finite} noncommutative geometries. Employing GW relation, we can prove the index theorem and construct topological invariants even if the system has only finite degrees of freedom. As an example, we consider a gauge theory on a fuzzy two-sphere and give an explicit construction of a noncommutative analog of the GW relation, chirality operator and the index theorem. The topological… 

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