Functional approaches such as Dyson-Schwinger equations and the
functional renormalisation group
offer a concise access to the physics underlying many non-perturbative
phenomena as well as a means for
reaching quantitative results. This access is achieved via the solution
of coupled sets of diagrammatic equations for
full gauge-fixed QCD correlation functions. For these tasks, the gauge
fixing rather allows for a convenient
reparameterisation rather than being a liability, and provides direct
access to the key QCD phenomena of
confinement and chiral symmetry breaking.
The talk starts with a brief introduction to the computation of
correlation functions in gauge-fixed QCD
with Dyson-Schwinger equations and the functional renormalisation group,
mostly concentrating on the latter.
Specifically, we discuss the mechanism behind dynamical chiral symmetry
breaking and show that its occurrence
is directly related to the strong coupling exceeding a critical value.
It is also shown that in covariant gauges
confinement, or the occurrence of a physical mass gap in Yang-Mills
theory or QCD, is directly related to a mass
gap in the gluonic propagator.
