  The infrared behavior of propagators and vertices is derived for the
maximally Abelian gauge and the Gribov-Zwanziger action relying on functional
equations. The derivation and analysis of Dyson-Schwinger equations increase
considerably in complexity when going beyond the standard Landau gauge fixing
and the available tools have to be improved. For the derivation of the
equations a computer program (DoDSE) was developed in order to handle the
plethora of terms. The process of determining possible infrared solutions is
abstracted to obtain further insight into the structure of the so-called
infrared scaling solutions. It is found that a few simple steps suffice to
determine possible infrared scaling relations directly from the action. For the
maximally Abelian gauge an infrared enhanced diagonal gluon propagator is
found, while the off-diagonal degrees of freedom are infrared suppressed. This
is in agreement with the idea of Abelian infrared dominance. Furthermore, it is
proven that SU(2) and higher SU(N) have the same infrared behavior, although
the corresponding actions differ. Under a suitable truncation the
Dyson-Schwinger equations are solved in the deep infrared to obtain values for
the exponents of the power laws. Restricting the integration in field
configuration space to the Gribov region of the Landau gauge with the
Gribov-Zwanziger action leads to two qualitatively equivalent infrared
solutions. In both cases the gluon propagator is infrared suppressed and the
infrared enhanced ghost propagator dominates the Dyson-Schwinger equations.
This result corroborates the conjecture by Zwanziger that the functional
integration can be cut at the first Gribov horizon and only the applied
boundary conditions are important. For one solution the Dyson-Schwinger
equations reduce in the deep infrared exactly to those obtained with the usual
Faddeev-Popov gauge fixing.
