Axial vector current of exact chiral symmetry on the lattice
  We discuss 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 \gamma_5 (1-aD), is explicitly constructed in the case of the Neuberger-Dirac operator. We also consider an Euclidean proof of the Nambu-Goldstone theorem using the Ward-Takahashi identity of this symmetry. 
Yoshio Kikukawa (Kyoto Univ.) and Atsushi Yamada (Univ. of Tokyo)