  The n-point Green functions of Landau gauge QCD are systematically
investigated in a Dyson-Schwinger approach assuming a static linearly rising
potential between fundamental color charges. Besides quarks also scalar matter
in the fundamental representation is considered. Starting from the hypothesis
of an 1/k^4 infrared divergent matter-antimatter vertex restrictions on the
general color tensor structure of this divergence are derived. Consequences for
the other four-point functions of QCD, resp., scalar QCD, are presented. Hereby
Casimir scaling is found. It is shown that possible singular contributions to
the three-point functions vanish due to cancellations within the color algebra.
On the other hand, higher n-point functions inherit the infrared singularity of
the matter-antimatter vertex in certain color channels. The presented results
show that linear confinement is consistently possible in a Greens function
approach, however, at the expense that the decoupling theorem is circumvented
by infrared singularities.
