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Lattice Landau gauge and other related lattice gauge fixing schemes are knownto violate spectral positivity. The most direct sign of the violation is therise of the effective mass as a function of distance. The origin of thisphenomenon lies in the quenched character of the auxiliary field $g$ used toimplement 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 covariantgauges similar to the one-parameter class of covariant gauges commonly used incontinuum gauge theories. Soluble models are used to illustrate the origin ofthe 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 typefirst studied by Fradkin and Shenker. The gluon propagator is interpreted asyielding bound states in the confined phase, and a mixture of fundamentalparticles in the Higgs phase, but lattice simulation shows the two phases areconnected. Gauge field propagators from the simulation of an SU(2) latticegauge theory on a $20^4$ lattice are well described by a quenched mass-mixingmodel. The mass of the lightest state, which we interpret as the gluon mass,appears to be independent of $\alpha$ for sufficiently large $\alpha$.Comment: 28 pages, 14 figures, RevTeX

Lattice gauge fixing as quenching and the violation of spectral positivity