  We calculate the lattice quark propagator in Coulomb gauge both from
dynamical and quenched configurations. We show that in the continuum limit both
the static and full quark propagator are multiplicatively renormalizable. From
the propagator we extract the quark renormalization function Z(|p|) and the
running mass M(|p|) and extrapolate the latter to the chiral limit. We find
that M(|p|) practically coincides with the corresponding Landau gauge function
for small momenta. The computation of M(|p|) can be however made more efficient
in Coulomb gauge; this can lead to a better determination of the chiral mass
and the quark anomalous dimension. Moreover from the structure of the full
propagator we can read off an expression for the dispersion relation of quarks,
compatible with an IR divergent effective energy. If confirmed on larger
volumes this finding would allow to extend the Gribov-Zwanziger confinement
mechanism to the fermionic sector of QCD.
