  Lattice Landau gauge and other related lattice gauge fixing schemes are known
to violate spectral positivity. The most direct sign of the violation is the
rise of the effective mass as a function of distance. The origin of this
phenomenon lies in the quenched character of the auxiliary field $g$ used to
implement lattice gauge fixing, and is similar to quenched QCD in this respect.
This is best studied using the PJLZ formalism, leading to a class of covariant
gauges similar to the one-parameter class of covariant gauges commonly used in
continuum gauge theories. Soluble models are used to illustrate the origin of
the violation of spectral positivity. The phase diagram of the lattice theory,
as a function of the gauge coupling $\beta$ and the gauge-fixing parameter
$\alpha$, is similar to that of the unquenched theory, a Higgs model of a type
first studied by Fradkin and Shenker. The gluon propagator is interpreted as
yielding bound states in the confined phase, and a mixture of fundamental
particles in the Higgs phase, but lattice simulation shows the two phases are
connected. Gauge field propagators from the simulation of an SU(2) lattice
gauge theory on a $20^4$ lattice are well described by a quenched mass-mixing
model. The mass of the lightest state, which we interpret as the gluon mass,
appears to be independent of $\alpha$ for sufficiently large $\alpha$.
