The Ghost-Gluon Vertex in Landau Gauge Yang-Mills Theory

Possible mechanisms for gluon confinement in Yang-Mills theory in covariant gauges are discussed briefly. Implications for the infrared behavior of the Green's functions are outlined. Results for the gluon and Faddeev-Popov ghost propagators from Dyson-Schwinger studies and lattice calculations are presented. The importance of the ghost-gluon vertex in these studies is discussed. Numerical results for a non-perturbatively constructed ghost-gluon vertex in four and three space-time dimensions are presented.