Spectrum of the Wilson Dirac operator at finite lattice spacings

Journal Article · Fri Apr 15 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.085014· OSTI ID:21541534

Akemann, G; Damgaard, P H; Splittorff, K; Verbaarschot, J J. M. ^[1]

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1. Department of Mathematical Sciences and BURSt Research Centre, Brunel University West London, Uxbridge UB8 3PH (United Kingdom)

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral random matrix theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.

• OSTI ID: 21541534
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRALITY
DIRAC OPERATORS
DISTRIBUTION
EIGENVALUES
FUNCTIONS
LAGRANGIAN FUNCTION
MATHEMATICAL OPERATORS
PARTICLE PROPERTIES
PERTURBATION THEORY
QUANTUM OPERATORS
RANDOMNESS
SPECTRA
SPECTRAL DENSITY
SPECTRAL FUNCTIONS