1998/12/31 by F. Farchioni, Ivan Hip, I. Hip +3 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dirac operator #Eigenvalues and eigenvectors #Fermion #Gauge theory #Hermitian matrix #Lattice (music) #Massless particle #Mathematical physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Theoretical physics #hep-lat #hep-ph
paper · pdf · doi:10.1016/s0550-3213(99)00162-5
published as Nucl.Phys. B549 (1999) 364-388 · 13 figures, 33 pages; minor changes, update to version accepted for publication
arxiv created 1999/04/30 · openalex publication_date 1999/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate.