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

Alkofer, Reinhard; Smekal, Lorenz von

doi:10.1016/s0370-1573(01)00010-2

Cited by 1,023 publications

(995 citation statements)

References 314 publications

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“…As they have no immediate consequences for the following sections we will refrain here to discuss aspects of the manifestations of confinement such as the analytic properties of the Green's functions of the theory or the structure of its asymptotic state space but refer to [147]. An approach that strengthens the evidence for confinement being related to the behaviour of Green's function in the extreme infrared only is based on the study of the gluon's quantum equation of motion and how its saturation in the infrared by physical or unphysical degrees of freedom distinguishes between the Coulomb, the Higgs and the confining phase of a gauge theory [148].…”

Section: Confinementmentioning

confidence: 99%

“…Dyson-Schwinger equations [184][185][186] are the quantum equations of motion of a quantum field theory; see [147,[187][188][189][190][191][192] for reviews of their applications to QCD. The starting point for the derivation of DSEs is the same as in lattice QCD, namely the generating functional or partition function (3.10).…”

Section: Dyson-schwinger Equations (Dses)mentioning

confidence: 99%

“…From the effective action one can derive the Dyson-Schwinger equations by taking further functional derivatives, see e.g. [147,187] for details, and the resulting equations relate the various 1PI Green functions to each other.…”

Section: Dyson-schwinger Equations (Dses)mentioning

confidence: 99%

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Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

405

503

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Confinementmentioning

confidence: 99%

Section: Dyson-schwinger Equations (Dses)mentioning

confidence: 99%

See 1 more Smart Citation

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

405

503

View full text Add to dashboard Cite

show abstract

“…In this scheme, the covariant diquark-quark model, see refs. [9][10][11][12][13][14][15][16], we obtain a tractable set of equations for the components of the covariant nucleon wave function which can be solved without non-relativistic reductions.…”

Section: Long Write-up 1 the Physical Problemmentioning

confidence: 99%

“…Inserting the ansatz (9) with the diquark pole contributions (10,11) into in the inhomogeneous equation (15) implicitly fixes the normalizations adopted for the diquark amplitudes. These implicit conditions are most easily derived from the derivative of eq.…”

Section: The Separable Approximation To the Relativistic 3-quark Problemmentioning

confidence: 99%

Relativistic three-quark bound states in separable two-quark approximation

Oettel

Smekal

Alkofer

2002

Computer Physics Communications

Self Cite

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Baryons as relativistic bound states in 3-quark correlations are described by an effective Bethe-Salpeter equation when irreducible 3-quark interactions are neglected and separable 2-quark correlations are assumed. We present an efficient numerical method to calculate the nucleon mass and its covariant wave function in this quantum field theoretic quark-diquark model with quark-exchange interaction. Expanding the components of the spinorial wave function in terms of Chebyshev polynomials, the four-dimensional integral equations are in a first step reduced to a coupled set of one-dimensional ones. This set of linear and homogeneous equations defines a generalised eigenvalue problem. Representing the eigenvector corresponding to the largest eigenvalue, the Chebyshev moments are then obtained by iteration. The nucleon mass is implicitly determined by the eigenvalue, and its covariant wave function is reconstructed from the moments within the Chebyshev approximation.

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Ghost-Free APT Analysis of Perturbative QCD Observables

Shirkov

2003

Particle Physics in the New Millennium

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We establish direct connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions.By combining the trick of resummation of the π 2 -terms for the invariant QCD coupling and observables in the time-like region with fresh results on the "analyticized" coupling α an (Q 2 ) and observables in the space-like domain we formulate a self-consistent scheme, free of ghost troubles. The basic point of this joint construction is the "dipole spectral relation" (1) emerging from axioms of local QFT.Then we consider the issue of the heavy quark thresholds and devise a global scheme for the data analysis in the whole accessible space-like and time-like domain with various numbers of active quarks. Observables in both the regions are presented in a form of non-power perturbation series with improved convergence properties.Preliminary estimates indicate that this global scheme produces results a bit different -on a few per cent level forᾱ s -from the usual one, thus influencing the total picture of the QCD parameters correlation.

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

Cited by 1,023 publications

References 314 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Relativistic three-quark bound states in separable two-quark approximation

Ghost-Free APT Analysis of Perturbative QCD Observables

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