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In a functional approach to QCD the infrared behaviour of Landau gauge Greenfunctions is investigated. Positivity violation for, and thus confinement of,gluons is demonstrated, and the analytic structure of the gluon propagator isstudied. Quark confinement is related to an infrared divergence of thequark-gluon vertex. In the latter various components are dynamically induceddue to the spontaneous breaking of chiral symmetry. As a result an infraredfinite running coupling in the Yang-Mills sector is derived whereas the runningcoupling related to the quark-gluon vertex is infrared divergent. Based on atruncation for the quark-gluon vertex Dyson-Schwinger equation, which respectsthe analytically determined infrared behavior, numerical results for thecoupled system of the quark propagator and vertex Dyson-Schwinger equations arepresented. The resulting quark mass function as well as the vertex functionshow only a very weak dependence on the current quark mass in the deepinfrared. From this we infer by an analysis of the quark-quark scatteringkernel a linearly rising quark potential with an almost mass independent stringtension in the case of broken chiral symmetry.

Confinement and Green functions in Landau-gauge QCD