  We investigate the infrared limit of the quantum equation of motion of the
gauge boson propagator in various gauges and models with a BRST symmetry. We
find that the saturation of this equation at low momenta distinguishes between
the Coulomb, Higgs and confining phase of the gauge theory. The Coulomb phase
is characterized by a massless gauge boson. Physical states contribute to the
saturation of the transverse equation of motion of the gauge boson at low
momenta in the Higgs phase, while the saturation is entirely due to unphysical
degrees of freedom in the confining phase. This corollary to the Kugo-Ojima
confinement criterion in linear covariant gauges also is sufficient for
confinement in general covariant gauges with BRST- and anti-BRST symmetry,
maximal Abelian gauges with an equivariant BRST symmetry, non-covariant Coulomb
gauge and in the Gribov-Zwanziger theory.
