Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
نویسندگان
چکیده
We show that the Ginsparg-Wilson (GW) relation can play an important role to define chiral structures in 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 invariant is shown to coincide with the 1st Chern class in the commutative limit.
منابع مشابه
Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus
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