Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

Details Chiral symmetry and spectrum of Euclidean Dirac operator in QCD Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

1995-03-08

arxiv.org/abs/hep-th/9503049v3

Physics

High Energy Physics

High Energy Physics - Theory

Invited talk on the Conference "Chiral Dynamics in Hadrons and Nuclei", Seoul, February, 1995. LaTeX file, 16 pages. 3 figures

Scientific paper

Some exact relations for the spectral density $\rho(\lambda)$ of the Euclidean Dirac operator in $QCD$ are derived. They follow directly from the chiral symmetry of the $QCD$ lagrangian with massless quarks. New results are obtained both in thermodynamic limit when the Euclidean volume $V$ is sent to infinity and also in the theory defined in finite volume where the spectrum is discrete and a nontrivial information on $\rho(\lambda)$ in the region $\lambda \sim 1/(|<\bar{q}q>_0|V)$ (the characteristic level spacing) can be obtained. These exact results should be confronted with "experimental" numerical simulations on the lattices and in some particular models for $QCD$ vacuum structure and may serve as a nontrivial test of the validity of these simulations.

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