Dyson-Schwinger equations and their application to hadronic physics

1994/01/01 by Craig D. Roberts, C. D. Roberts, Anthony G. Williams +1 · 60 citations
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th

paper · pdf · doi:10.1016/0146-6410(94)90049-3

published as Prog.Part.Nucl.Phys.33:477-575,1994 · 110 pages, LaTeX. Replaced only to facilitate retrieval. Also available at /u/ftp/pub/Review.uu via anonymnous-ftp

openalex publication_date 1994/01/01 · arxiv created 1997/08/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions.

Citations

• Introduction to Gauge Field Theory
• Quantization of non-Abelian gauge theories
• Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics
• Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I
• On the generalized ward identity
• Dynamical mass generation in continuum quantum chromodynamics
• Gauge covariant fermion propagator in quenched, chirally symmetric quantum electrodynamics
• Infrared singularities and massive fields
• Effective action for composite operators
• Review of particle properties
• Quark masses

Cited by

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• Chiral symmetry breaking in dimensionally regularized nonperturbative quenched QED
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• Charge symmetry breaking via ϱω mixing from model quark-gluon dynamics
• Renormalized strong-coupling quenched QED in four dimensions
• Renormalization and chiral symmetry breaking in quenched QED in arbitrary covariant gauges
• Regularization-independent study of renormalized nonperturbative quenched QED
• Nonperturbative improvement and tree-level correction of the quark propagator
• Quark propagator in the Landau gauge
• General Algorithm for Improved Lattice Actions on Parallel Computing Architectures
• Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach
• Decay constants of the pion and B mesons with the Bethe–Salpeter equation
• Quark-antiquark bound states within a Dyson-Schwinger Bethe-Salpeter formalism
• Confinement, monopoles and Wilsonian effective action
• Exotic hadrons with heavy flavors: X, Y, Z, and related states
• Infrared exponents and the strong-coupling limit in lattice Landau gauge
• Structure and decay constant of the ρ meson within the Bethe-Salpeter equation
• Yang-Mills two-point functions in linear covariant gauges
• Quark number susceptibility around the critical end point
• Evidence for Instanton-Induced Dynamics from Lattice QCD
• Vector and axial-vector correlators in a non-local chiral quark model
• Quark propagator and chiral symmetry with string tension
• Chiral symmetry breaking and scalar string confinement
• Quark stars in strong magnetic fields
• Chiral Extrapolation of Lattice Data for Heavy Meson Hyperfine Splittings
• πandρmesons, and their diquark partners, from a contact interaction
• Approximating chiral quark models with linear σ-models
• Theory and phenomenology of hadrons
• From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance
• The pion: an enigma within the Standard Model
• Analysis of the X (1835) as a Baryonium State with the Bethe—Salpeter Equation
• Quark spectral density and strongly-coupled quark-gluon plasma
• Thermal renormalization group equations and the phase transition of scalarO<mml:mn/>(N)<mml:mn/>theories
• Semileptonic decays of double heavy baryons
• Quark gap equation within the analytic approach to QCD
• Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism
• Nonzero mean squared momentum of quarks in the nonperturbative QCD vacuum
• A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential
• Properties of effective massive Yang-Mills theory in the limit of vanishing vector boson mass
• The Wigner solution and QCD phase transitions in a modified PNJL model
• The two-particle-irreducible vertex of the two-dimensional lattice ϕ⁴ model across the Ising transition
• REMARK ON THE CONSISTENCY OF THE LADDER APPROXIMATION AND THE RAINBOW APPROXIMATION OF DYSON–SCHWINGER EQUATIONS OF QCD
• Light Baryon Spectroscopy
• Studies of the structure of massive hybrid stars within a modified NJL model
• Neutron star universal relations with microscopic equations of state
• Dispersive approach to QCD and hadronic contributions to electroweak observables
• Dynamical chiral symmetry breaking inQED3at finite density and impurity potential
• Confinement induced by fermion damping in three-dimensional QED
• Strong-Interaction Matter under Extreme Conditions from Chiral Quark Models with Nonlocal Separable Interactions
• Infrared and ultraviolet properties of the Landau gauge quark propagator
• Dynamical symmetry breaking, confinement with flat-bottom potential
• Does There Exist Only One Solution of the Dyson–Schwinger Equation for the Quark Propagator in the Case of Non-Zero Current Quark Mass
• Jülich-Bonn-Washington model for pion electroproduction multipoles
• Dynamical chiral symmetry breaking in effective models of QCD in the Bethe-Salpeter approach
• More on large-momentum effective theory approach to parton physics
• Light charged fermions in quantum gravity
• Non-Perturbative Analysis of Various Mass Generation by Gluonic Dressing Effect with the Schwinger-Dyson Formalism in QCD
• On the nonperturbative solution of Pauli–Villars-regulated light-front QED: A comparison of the sector-dependent and standard parameterizations
• Pion radiative weak decays in nonlocal chiral quark models
• Regimes of 3D Yang–Mills theory in the presence of a constant vector background