Prerequisites of confinement in the covariant and local description of QCD
are reviewed. In particular, the Kugo-Ojima confinement criterion, the
positivity violations of transverse gluon and quark states, and the conditions
necessary to avoid the decomposition property for colored clusters are
discussed. In Landau gauge QCD, the Kugo-Ojima confinement criterion follows
from the ghost Dyson-Schwinger equation if the corresponding Green's functions
can be expanded in an asymptotic series. Furthermore, the infrared behaviour of
the propagators in Landau gauge QCD as extracted from solutions to truncated
Dyson-Schwinger equations and lattice simulations is discussed in the light of
these issues.Comment: 8 pages, 5 figures; To be published in the proceedings of the
Workshop on Dynamical aspects of the QCD phase transition, ECT* Trento, March
12 - 15, 2001. Typos correcte
