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(k2) := 1/[1+Π(k2)], where Π(k2) 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(k2 = 0) = 0 and max(P(k2)) ∼ 10 neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of P(k2) via numerical simulations.