Quarks are the main constituents of protons and neutrons and hence
are important building blocks of all the matter that surrounds us.
However, quarks have the intriguing property that they never appear
as isolated single particles but only in bound states. This
phenomenon is called confinement and has been a central research
topic of elementary particle physics for the last few decades. In
order to find the mechanism that forbids the existence of free
quarks many approaches and ideas are being followed, but by now it
has become clear that they are not mutually exclusive but
illuminate the problem from different perspectives. Two such
confinement scenarios are investigated in this thesis: Firstly, the
importance of Abelian field components for the low-energy regime is
corroborated, thus supporting the dual superconductor picture of
confinement and secondly, the influence of the Gribov horizon on
non-perturbative solutions is studied.
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