Schwinger-Dyson Equations in Coulomb Gauge Consistent with Numerical Simulation

Abstract

In the present work we undertake a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition ${\partial }_i{A}_i=0$. We continue a previous study which kept only instantaneous terms in the SDE that are proportional to $\delta (t)$ in order to calculate the instantaneous part of the time component of the gluon propagator $D_{A_0{A}_0}(t,R)$. We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1\% to 3\%. This raises the question, "Why is the agreement so good, despite the systematic neglect of non-instantaneous terms?" We discovered the happy circumstance that all the non-instantaneous terms are in fact zero. They are forbidden by the symmetry of the local action in Coulomb gauge under time-dependent gauge transformations $g(t)$. This remnant gauge symmetry is not fixed by the Coulomb gauge condition. The numerical result of the present calculation is the same as in the previous study; the novelty is that we now demonstrate that all the non-instantaneous terms in the SDE vanish. We derive some elementary properties of propagators which are a consequence of the remnant gauge symmetry. In particular the time component of the gluon propagator is found to be purely instantaneous $D_{A_0{A}_0}(t,R)=\delta (t)V(R)$, where $V(R)$ is the color-Coulomb potential. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, $V(R)\sim \sigma R$ at large $R$.

arXiv comment17 pages

References in corpus (38)

• Non-perturbative Landau gauge and infrared critical exponents in QCD
• The Gribov problem and QCD dynamics
• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• No confinement without Coulomb confinement
• Gluonic three-point correlations in pure Landau gauge QCD
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
• Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Numerical Study of the Ghost-Gluon Vertex in Landau gauge
• Infrared behaviour of the ghost-gluon vertex in Landau gauge Yang-Mills theory
• Constructing non-perturbative gauges using correlation functions
• Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• Propagators in Coulomb gauge from SU(2) lattice gauge theory
• Quark-Gluon Plasmas and Thermalization
• The Coulomb gauge ghost Dyson-Schwinger equation
• Towards a Theory of the QCD String
• Spectral properties of the Landau gauge Faddeev-Popov operator in lattice gluodynamics
• Infrared analysis of Dyson-Schwinger equations taking into account the Gribov horizon in Landau gauge
• Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
• Variational approach to Yang-Mills theory at finite temperatures
• Looking for Integrability on the Worldsheet of Confining Strings
• Ghost propagator and the Coulomb form factor from the lattice
• Non-perturbative analysis of the Gribov-Zwanziger action
• Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge
• Vertex functions of Coulomb gauge Yang--Mills theory
• Cancellation of energy-divergences in Coulomb gauge QCD
• Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
• Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory
• Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics
• Local QCD Action at Finite Temperature
• The Coulomb flux tube on the lattice
• Finiteness of the Coulomb gauge QCD perturbative effective action
• Origin of Confining Force
• The effective action in Coulomb gauge QCD
• Functional approaches to infrared Yang-Mills theory in the Coulomb gauge
• Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge

Cited by in corpus (2)

• Different faces of confinement
• The Coulomb flux tube revisited