The QCD Quark Propagator in Coulomb Gauge and - Institut für Physik

Chapter 3
Remarks on QCD in Coulomb Gauge
“Yet, despite its headstart in an Abelian context, application of the Coulomb gauge to non-
Abelian models remains as puzzling and problematic today as ever.“ This is a statement
of [Lei] and is probably still up to date. The present chapter is devoted to point out
that together with the difficulties outstanding features are connected to QCD in Coulomb
gauge.
3.1 Motivation
For many years Landau gauge has been the most popular choice for non-perturbative
QCD efforts. It imposes transversality of the gluon field in space-time and has proven to
be practical. Feynman rules can be derived easily, it preserves Lorentz invariance of the
theory and allows for simple ansätze in the truncation of the infinitely coupled system of
DSEs.
Considerable advances in DSE Landau gauge studies have been achieved over the last
years. For example in [Fis03] for the first time the coupled system of quark, gluon and
ghost DSEs was solved. Such studies support a possible infrared effective theory which is
given by the gauge-fixing parts of the action [Fis06]. Ghost degrees of freedom dominate in
the infrared and are responsible for long range correlations whereas the gluon propagator
vanishes at zero momentum. This property implies positivity violations in the gluon
propagator and assures that transverse gluons are confined. The infrared analysis of the
running coupling of SU(N)-Yang-Mills theory showed a fixed point which is qualitatively
universal and invariant in a class of transverse gauges. The quark propagator exhibits
dynamical chiral symmetry breaking and the chiral condensate can be extracted reliably.
In the meson sector of QCD the approach naturally reproduces both the Goldstone nature
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