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In the first part of this thesis a coupled truncated set of Dyson-Schwingerequations (DSEs) including the one for the gluon-propagator is solvedself-consistently over the whole momentum range. In Landau gauge the truncationof the coupled set of DSEs for the ghost and gluon propagators is improved bythe first full inclusion of the sunset diagram. A solution method which avoidsall overlapping divergences is presented. In the Maximal Abelian gauge atruncation is developed with respectively one infrared and one ultravioletleading diagram included. A first solution of the ghost equation is presented.In the second part generalizations of the Kugo-Ojima confinement scenario toother gauges than the linear covariant gauge are investigated. In thegeneralized covariant gauge no contradiction is found by using a Faddeev-Popovconjugation invariant assignment of the asymptotic fields. In the last sectiona gauge-independent generalized criterion is developed which allows for theidentification of the Coulomb, Higgs- and confining phases of Yang-Mills theoryin terms of the infrared limit of the Dyson-Schwinger equation of the gaugeboson propagator. While in a Coulomb phase the photon is massless, dominatingthe infrared of the equation, in the Higgs phase this equation is dominated bythe physical mass of the gauge boson. In the confining phase the equation issaturated by unphysical degrees of freedom in the infrared limit only. Thisproposal is tested in a variety of gauges and the corresponding unphysicalterms are identified.

Signals of Confinement in the Dyson-Schwinger Equation for the Gauge Boson Propagator