Axial vector current of exact chiral symmetry on the lattice

Abstract

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 γ_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.

14 pages, LaTeX2e, some corrections in references, typo fixed, a discussion of the property of the current kernel added

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• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• More about exactly massless quarks on the lattice
• The index theorem in QCD with a finite cut-off
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• Overlap in odd dimensions
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• Lattice QCD with Ginsparg-Wilson fermions
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• Lattice Chirality
• Renormalizability of a lattice chiral fermion in the overlap formulation
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