A new gauge fixing method for Abelian projection

Shoji, Fumiyoshi; Suzuki, Tsuneo; Kodama, Hiroaki; Nakamura, Atsushi

doi:10.1016/s0370-2693(00)00147-7

Cited by 11 publications

(16 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent results by Horsley and collaborators [339], α V (Q 2 ) and its β-function are computed on a lattice using numerical stochastic perturbation theory; see the reviews in Refs. [340,341] …”

Section: Lattice Results For α S In the Irmentioning

confidence: 99%

The QCD running coupling

Deur

Brodsky

Téramond

2016

Progress in Particle and Nuclear Physics

298

236

View full text Add to dashboard Cite

We review the present theoretical and empirical knowledge for α s , the fundamental coupling underlying the interactions of quarks and gluons in Quantum Chromodynamics (QCD). The dependence of α s (Q 2 ) on momentum transfer Q encodes the underlying dynamics of hadron physics -from color confinement in the infrared domain to asymptotic freedom at short distances. We review constraints on α s (Q 2 ) at high Q 2 , as predicted by perturbative QCD, and its analytic behavior at small Q 2 , based on models of nonperturbative dynamics. In the introductory part of this review, we explain the phenomenological meaning of the coupling, the reason for its running, and the challenges facing a complete understanding of its analytic behavior in the infrared domain.In the second, more technical, part of the review, we discuss the behavior of α s (Q 2 ) in the high momentum transfer domain of QCD. We review how α s is defined, including its renormalization scheme dependence, the definition of its renormalization scale, the utility of effective charges, as well as "Commensurate Scale Relations" which connect the various definitions of the QCD coupling without renormalization-scale ambiguity. We also report recent significant measurements and advanced theoretical analyses which have led to precise QCD predictions at high energy. As an example of an important optimization procedure, we discuss the "Principle of Maximum Conformality", which enhances QCD's predictive power by removing the dependence of the predictions for physical observables on the choice of theoretical conventions such as the renormalization scheme. In the last part of the review, we discuss the challenge of understanding the analytic behavior α s (Q 2 ) in the low momentum transfer domain. We survey various theoretical models for the nonperturbative strongly coupled regime, such as the light-front holographic approach to QCD. This new framework predicts the form of the quark-confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q 0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the GribovZwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of α s (Q 2 ) in order to bring better unity to the subject.2

show abstract

Section: Lattice Results For α S In the Irmentioning

confidence: 99%

The QCD running coupling

Deur

Brodsky

Téramond

2016

Progress in Particle and Nuclear Physics

298

236

View full text Add to dashboard Cite

show abstract

“…There are also recent numerical investigations on the lattice based on Stochastic Quantisation, e.g., see Refs. [95][96][97].…”

Section: Gribov Copies Monopoles and Gauge Fixingmentioning

confidence: 99%

The infrared behaviour of QCD Green's functions Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

2001

View full text Add to dashboard Cite

“…Stochastic quantization may be and has been exactly simulated numerically including on rather large lattices, of volume (48) 4 , [43], [44], [45], [46], [47].…”

Section: Review Of Stochastic Quantization Of Gauge Fieldsmentioning

confidence: 99%

Nonperturbative Faddeev-Popov formula and the infrared limit of QCD

2004

View full text Add to dashboard Cite

We show that an exact nonperturbative quantization of continuum gauge theory is provided by the Faddeev-Popov formula in the Landau gauge, ␦(‫•ץ‬A)det͓Ϫ‫•ץ‬D(A)͔exp͓ϪS YM (A)͔, restricted to the region where the Faddeev-Popov operator is positive Ϫ‫•ץ‬D(A)Ͼ0 ͑Gribov region͒. Although there are Gribov copies inside this region, they have no influence on expectation values. The starting point of the derivation is stochastic quantization which determines the Euclidean probability distribution P(A) by a method that is free of the Gribov critique. In the Landau-gauge limit the support of P(A) shrinks down to the Gribov region with Faddeev-Popov weight. The cutoff of the resulting functional integral on the boundary of the Gribov region does not change the form of the Dyson-Schwinger ͑DS͒ equations because det͓Ϫ‫•ץ‬D(A)͔ vanishes on the boundary, so there is no boundary contribution. However this cutoff does provide supplementary conditions that govern the choice of solution of the DS equations. In particular the ''horizon condition,'' though consistent with the perturbative renormalization group, puts QCD into a nonperturbative phase. The infrared asymptotic limit of the DS equations of QCD is obtained by neglecting the Yang-Mills action S YM . We sketch the extension to a BRST-invariant formulation. In the infrared asymptotic limit, the BRST-invariant action becomes BRST exact, and defines a topological quantum field theory with an infinite mass gap. Confinement of quarks is discussed briefly.

show abstract

A new gauge fixing method for Abelian projection

Cited by 11 publications

References 14 publications

The QCD running coupling

The QCD running coupling

The infrared behaviour of QCD Green's functions Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

Nonperturbative Faddeev-Popov formula and the infrared limit of QCD

Contact Info

Product

Resources

About