Gluon propagators and QCD vacuum

A non-perturbative study of gluon propagators on the lattice is reported for those who do not work with numerical simulations. We first review the U(1) case, and show that there "Gribov copies" and a residual gauge symmetry play an important role to get a massless propagator of the perturbative form. For SU(3), the propagators dhow the large deviation from those of massless gauge particles. They decrease rapidly at large euclidean distance, which matches with the phenomenological infinitely heavy mass. The propagators seem to have no physical pole, but we need more study to confirm their infra-red behavior.