GinspargWilson relation, topological invariants, and finite noncommutative geometry
Abstract
We show that the GinspargWilson (GW) relation can play an important role in defining chiral structures in finite noncommutative geometries. Employing the 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 twosphere and give an explicit construction of a noncommutative analogue of the GW relation, chirality operator, and the index theorem. The topological invariant is shown to coincide with the first Chern class in the commutative limit.
 Publication:

Physical Review D
 Pub Date:
 April 2003
 DOI:
 10.1103/PhysRevD.67.085005
 arXiv:
 arXiv:hepth/0209223
 Bibcode:
 2003PhRvD..67h5005A
 Keywords:

 11.10.Nx;
 11.15.Ha;
 11.15.Tk;
 11.30.Rd;
 Noncommutative field theory;
 Lattice gauge theory;
 Other nonperturbative techniques;
 Chiral symmetries;
 High Energy Physics  Theory;
 High Energy Physics  Lattice;
 Mathematical Physics;
 Mathematics  Quantum Algebra
 EPrint:
 Revtex4 file, 5 pages, references added, typo corrected, the final version to appear in Phys.Rev.D