The analysis of space-time structure in QCD vacuum II: Dynamics of polarization and absolute X-distribution

Journal Article · Mon Aug 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.007· OSTI ID:21583323

Alexandru, Andrei ^[1]; Draper, Terrence; Horvath, Ivan ^[2]; Streuer, Thomas ^[3]

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1. Department of Physics, George Washington University, Washington, DC 20052 (United States)
2. Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506 (United States)
3. Department of Physics, University of Regensburg, 93040 Regensburg (Germany)

Highlights: > We propose a method to compute the polarization for a multi-dimensional random distribution. > We apply the method to the eigenemodes of the Dirac operator in pure glue QCD. > We compute the chiral polarization for these modes and study its scale dependence. > We find that in a finite volume there is a scale where the polarization tendency changes. > We study the continuum limit of this chiral polarization scale. - Abstract: We propose a framework for quantitative evaluation of dynamical tendency for polarization in an arbitrary random variable that can be decomposed into a pair of orthogonal subspaces. The method uses measures based on comparisons of given dynamics to its counterpart with statistically independent components. The formalism of previously considered X-distributions is used to express the aforementioned comparisons, in effect putting the former approach on solid footing. Our analysis leads to the definition of a suitable correlation coefficient with clear statistical meaning. We apply the method to the dynamics induced by pure-glue lattice QCD in local left-right components of overlap Dirac eigenmodes. It is found that, in finite physical volume, there exists a non-zero physical scale in the spectrum of eigenvalues such that eigenmodes at smaller (fixed) eigenvalues exhibit convex X-distribution (positive correlation), while at larger eigenvalues the distribution is concave (negative correlation). This chiral polarization scale thus separates a regime where dynamics enhances chirality relative to statistical independence from a regime where it suppresses it, and gives an objective definition to the notion of 'low' and 'high' Dirac eigenmode. We propose to investigate whether the polarization scale remains non-zero in the infinite volume limit, in which case it would represent a new kind of low energy scale in QCD.

• OSTI ID: 21583323
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 8; Other Information: DOI: 10.1016/j.aop.2011.04.007; PII: S0003-4916(11)00066-2; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRALITY
CORRELATIONS
DIRAC OPERATORS
DISTRIBUTION
EIGENVALUES
GAUGE INVARIANCE
HIGH ENERGY PHYSICS
POLARIZATION
QUANTUM CHROMODYNAMICS
RANDOMNESS
SOLIDS
SPACE-TIME
SPECTRA
FIELD THEORIES
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
PARTICLE PROPERTIES
PHYSICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS