The Coulomb gauge ghost Dyson-Schwinger equation

Abstract

A numerical study of the ghost Dyson-Schwinger equation in Coulomb gauge is performed and solutions for the ghost propagator found. As input, lattice results for the spatial gluon propagator are used. It is shown that in order to solve completely, the equation must be supplemented by a nonperturbative boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (critical) solution when going from high to low momenta until `forced' to freeze out in the infrared to the value of the boundary condition. The renormalization is shown to be largely independent of the boundary condition. The boundary condition and the pattern of the solutions can be interpreted in terms of the Gribov gauge-fixing ambiguity. The connection to the temporal gluon propagator and the infrared slavery picture of confinement is explored.

17 pages, 5 figures, updated version to account for referees' suggestions

References in corpus (41)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Infrared Properties of QCD from Dyson-Schwinger equations
• On the infrared behavior of Landau gauge Yang-Mills theory
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• On the Infrared Exponent for Gluon and Ghost Propagation in Landau Gauge QCD
• A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
• Coulomb Gauge QCD, Confinement, and the Constituent Representation
• On the IR behaviour of the Landau-gauge ghost propagator
• Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• Constraints on the IR behavior of the ghost propagator in Yang-Mills theories
• Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
• Mesons in a Poincare Covariant Bethe-Salpeter Approach
• IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation
• Coulomb gauge gluon propagator and the Gribov formula
• Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
• Constructing non-perturbative gauges using correlation functions
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• QCD in the Infrared with Exact Angular Integrations
• Lattice Coulomb Hamiltonian and Static Color-Coulomb Field
• Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit
• Propagators in Coulomb gauge from SU(2) lattice gauge theory
• Numerical Study of Gluon Propagator and Confinement Scenario in Minimal Coulomb Gauge
• Dielectric function of the QCD vacuum
• Renormalization-group Calculation of Color-Coulomb Potential
• Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
• Two-Point Functions of Coulomb Gauge Yang-Mills Theory
• Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
• Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
• Resolving temporal Gribov copies in Coulomb gauge Yang-Mills theory
• Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
• Coulomb gauge confinement in the heavy quark limit
• Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory
• Quarks in Coulomb gauge perturbation theory
• Perturbation theory in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• Faddeev-Popov spectra at the Gribov horizon
• Cancellation of energy-divergences and renormalizability in Coulomb gauge QCD within the Lagrangian formalism

Cited by in corpus (37)

• The Infrared Behaviour of the Pure Yang-Mills Green Functions
• On the zero crossing of the three-gluon vertex
• Effects of divergent ghost loops on the Green's functions of QCD
• On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions
• Refining the detection of the zero crossing for the symmetric and asymmetric three-gluon vertices
• The lattice gluon propagator in renormalizable $\xi$ gauges
• Discretization effects on renormalized gauge-field Green's functions, scale setting and gluon mass
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Nonperturbative study of the four gluon vertex
• Schwinger mechanism in linear covariant gauges
• Leading order infrared quantum chromodynamics in Coulomb gauge
• Nonperturbative structure of the ghost-gluon kernel
• Unified description of seagull cancellations and infrared finiteness of gluon propagators
• Nearly perturbative lattice-motivated QCD coupling with zero IR limit
• Are the Dressed Gluon and Ghost Propagators in the Landau Gauge presently determined in the confinement regime of QCD?
• Variational approach to Yang-Mills theory at finite temperatures
• The gluon propagator in linear covariant $R_{\xi }$ gauges
• Comment on "Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure $SU(3)$ Yang-Mills Theory: Finite Lattice Spacing and Volume Effects"
• Ghost propagator and the Coulomb form factor from the lattice
• On bounds and boundary conditions in the continuum Landau gauge
• Calculation of the non-perturbative strong coupling from first principles
• One-loop RG improvement of the screened massive expansion in the Landau gauge
• The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge
• Dimension two condensates in the Gribov-Zwanziger theory in the Coulomb gauge
• Dyson-Schwinger approach to strongly coupled theories
• Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics
• A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges
• The Nielsen identities in screened theories
• Analytic continuation and physical content of the gluon propagator
• The gluon mass generation mechanism: a concise primer
• Schwinger-Dyson Equations in Coulomb Gauge Consistent with Numerical Simulation
• Screened massive expansion of Schwinger-Dyson equations
• The Coulomb flux tube revisited
• Quark sector of Coulomb gauge Quantum Chromodynamics
• Schwinger-Dyson type equations for some QFT models
• Dyson--Schwinger Approach to Hamiltonian QCD
• Vertex Sensitivity in the Schwinger-Dyson Equations of QCD