1998/08/31 by Yoshio Kikukawa, Atsushi Yamada · 49 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chiral symmetry #Chiral symmetry breaking #Current (fluid) #Dirac operator #Euclidean geometry #Geometry #Lattice (music) #Lattice QCD #Lattice field theory #Mathematical physics #Mathematics #Operator (biology) #Physics #Pseudovector #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Symmetry (geometry) #hep-lat
paper · pdf · doi:10.1016/s0550-3213(99)00059-0
published in Nuclear Physics B 547(1-2), 413-423 (Elsevier BV) · 14 pages, LaTeX2e, some corrections in references, typo fixed, a discussion of the property of the current kernel added
arxiv created 1998/09/08 · openalex publication_date 1999/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 γ5 (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.