Infrared behaviour of propagators and vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by P(k(2)): = 1/[1 + Pi(k(2))], where Pi(k(2)) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest P(k(2) = 0)= 0 and max(P(k(2))) similar to 10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k(2)) via numerical simulations. (C) 1998 Published by Elsevier Science B.V. All rights reserved.