Some remarks on the Ginsparg-Wilson fermion
arXiv:hep-lat/0005005 · doi:10.1016/S0550-3213(00)00493-4
Abstract
We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson relation is equivalent to setting $R = (a γ_5 D)^{2k}$ in the original Ginsparg-Wilson relation $D γ_5 + γ_5 D = 2 a D R γ_5 D$. An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order (k > 0) realizations of Overlap Dirac operator are compared to those of the Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial anomaly and the fermion determinant in a background gauge field. Our present results (up to lattice size 16 x 16) indicate that the chiral properties of the Neuberger-Dirac operator are better than those of higher-order ones.
20 pages, minor changes in v3, to appear in Nucl. Phys. B