Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

A. Smilga

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arXiv · hep-th/9503049

Chiral symmetry and spectrum of Euclidean Dirac operator in QCD

A. Smilga

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Abstract

Some exact relations for the spectral density $ρ(λ)$ 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 $ρ(λ)$ in the region $λ\sim 1/(|<\bar{q}q>_0|V)$ (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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A. Smilga. 1995-11-29. Chiral symmetry and spectrum of Euclidean Dirac operator in QCD. https://arxiv.org/abs/hep-th/9503049

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