Axial vector current of exact chiral symmetry on the lattice Original Research Article

We consider the exact chiral symmetry and its spontaneous breakdown in lattice QCD with the Dirac operators satisfying the Ginsparg-Wilson relation. The axial vector current, which turns out to be related to the vector current simply by the insertion of the operator γ5 (1 − aD), is explicitly constructed in the cases of the Neuberger-Dirac operator and its rational approximation. We also discuss a Euclidean proof of the Nambu-Goldstone theorem using the axial Ward-Takahashi identity of this symmetry.