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

Running mass, effective energy and confinement: the lattice quark propagator in Coulomb gauge