A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Study of the gluon propagator in the axial gauge

It is shown that a non-linear integral equation for the gluon propagator in the axial gauge (Baker et al.) can be simplified considerably. A comparison is made with an approximate equation for the gluon propagator in the Landau gauge (Mandelstam). Both equations have polynomial kernels where the argument is the divisor of the internal and external momenta. A solution which behaves as a double pole for low momenta remains consistent.     

The gluon propagator in the Coulomb gauge

We give the results for all the one-loop propagators, including finite parts, in the Coulomb gauge. In the finite parts we find new non-rational functions in addition to the single logarithms of the Feynman gauge. Of course, the two gauges must agree for any gauge invariant function.Received: 14 November 2003, Revised: 20 July 2004, Published online: 24 September 2004     

Infrared effects on the axial gauge quark propagator

The axial gauge quark propagator is studied when only the most singular infrared part of the gluon propagator is retained in the Dyson-Schwinger equation. With a new representation for the quark-gluon vertex a simple configuration space propagator and a momentum space form valid for all values of the gauge variable n · p are obtained. The propagator has no poles. The effective potential is minimized when there is no chiral symmetry breaking.     

Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory. (II) The gluon propagator in Landau gauge

This is the second of two papers devoted to the perturbative computation of the ghost and gluon propagators in SU(3)$\mathit{SU}(3)$ Lattice Gauge Theory. Such a computation should enable a comparison with results from lattice simulations in order to reveal the genuinely non-perturbative content of the latter. The gluon propagator is computed by means of Numerical Stochastic Perturbation Theory: results range from two up to four loops, depending on the different lattice sizes. The non-logarithmic constants for one, two and three loops are extrapolated to the lattice spacing a→0$a\to 0$ continuum and infinite volume V→∞$V\to \infty$ limits.     

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of S?o Paulo.     

Numerical calculation of the momentum-space gluon propagator in quenched,reduced QCD3

A recently developed method of momentum-space Monte Carlo is applied to compute the momentum-space gluon propagator in quenched, reduced, continuum QCD₃ in axial gauge. There is some evidence that the gluon propagator D_μν(p) is finite as p → 0, which might indicate the existence of a non-perturbative gluon mass.     

Summary of working group activities in non-perturbative quantum chromodynamics (lattice gauge theory)

We summarize the activities of the lattice gauge theory section of the working group activities in non-perturbative QCD.     

The refractive properties of the gluon plasma in SU(2) gauge theory

New representations of the total probability of radiation and of the radiative energy loss for charged particle moving in an arbitrary extenal field are obtained in the frame of the quasiclassical operator approach in the quantum electrodynamics. From general results new representations of the total probability and the total intensity of the magnetic bremsstrahlung are derived. The polarization of the radiation, radiation of polarized electrons and radiative polarization have been considered as well.     

Linear response of the hot QCD plasma from the gluon propagator

Linear response theory is used to express the positions of the physical poles in the finite temperature gluon propagator in terms of the components of the proper self-energy. The analysis is valid in a wide class of covariant and non-covariant gauges, for both transverse and non-transverse self-energies. The formalism is then applied to the calculation at the one loop level of the bare plasma parameters and of Landau ghosts in two classes of gauges: the covariant gauge and a one parameter family of non-covariant gauges which interpolate between the static temporal gauge and the Coulomb gauge.     

Ultraviolet and infrared aspects of the axial anomaly II

This is the second part of a brief review of some perturbative aspects of the Adler-Bell-Jackiw axial anomaly. To begin with, we discuss here the derivation of the anomaly based on the imaginary part of the VVA triangle graph and dispersion relations. Within such an approach the infrared properties of the VVA amplitude are substantial. Next we summarize the main results obtained by the present author and co-authors concerning some particular ultraviolet and infrared aspects of the axial anomaly. These results cover a wide variety of topics, ranging from dispersion relations to a systematic analysis of gauge invariant ultraviolet regularizations of the VVA triangle graph. In the latter context, one of the highlights is a reinterpretation of dimensional regularization of the VVA diagram as a continuous superposition of Pauli-Villars cut-offs.     

A Gauge and Lorentz covariant approximation for the quark propagator in an arbitrary gluon field

We decompose the quark propagator in the presence of an arbitrary gluon field with respect to a set of Dirac matrices. The four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integrals along certain field lines, together with a weighted integration over the various field lines. It is then easy to transform the propagator into a form involving path ordered exponentials. The resulting expression is non-perturbative and has the correct behavior under Lorentz transformations, gauge transformations and charge conjugation. Furthermore it coincides with the exact propagator in first order of the coupling g. No expansion with respect to the inverse quark mass is involved, the expression can even be used for vanishing mass. For large mass the field lines concentrate near the straight line connection and simple results can be obtained immediately. Received: 31 March 2001 / Revised version: 3 May 2001 / Published online: 8 June 2001     

Variational calculation of SU(2) quantum gauge fields

The SU(2) Yang-Mills quantum field is studied by Coulomb-gauge continuum-hamiltonian methods using a variational approximation. The field amplitudes are represented by a truncated momentum expansion in the spatial domain S³. The calculations support Gribov's scenario for the generation of a mass gap in the spectrum of physical states and the confinement of color.