Axial vector current of exact chiral symmetry on the lattice

We consider the exact chiral symmetry and its spontaneous breakdown in latt ice QCD with the Dirac operators satisfying the Ginsparg-Wilson relation. T he axial vector current, which turns out to be related to the vector curren t simply by the insertion of the operator gamma(5)(1 - aD), is explicitly c onstructed in the cases of the Neuberger-Dirac operator and its rational ap proximation. We also discuss a Euclidean proof of the Nambu-Goldstone theor em using the axial Ward-Takahashi identity of this symmetry. (C) 1999 Elsev ier Science B.V.