Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2002-05-23
Int.J.Mod.Phys. B16 (2002) 1931-1942
Physics
High Energy Physics
High Energy Physics - Lattice
11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical Physics, Tianjin, China, 8-11 Octo
Scientific paper
10.1142/S0217979202011652
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been established yet. We suggest that the Wilsonian effective action is essential to avoid infrared singularities encountered in general perturbative analyses.
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