  We discuss the properties of ghost and gluon propagators in Landau gauge
Yang-Mills theory and their relation to the confinement problem. In general two
types of infrared behavior of these functions are allowed from their functional
equations: scaling and decoupling. Both solutions show positivity violations in
the gluon propagator and lead to a confining Polyakov loop potential. However,
only the scaling solution agrees with the Kugo-Ojima confinement scenario and
the related formulation of a physical Hilbert space of Yang-Mills theory. Our
numerical results for the gluon dressing function agree almost pointwise with
the lattice results at all physical momenta.
