The gluon propagator in Coulomb gauge from the lattice

We show that in the lattice Hamiltonian limit the static transverse propagator $D(\mathrm{\mid }\vec{p}\mathrm{\mid })\propto \int d{p}_{0}D(\mathrm{\mid }\vec{p}\mathrm{\mid },p_0)$ satisfies multiplicative renormalizability. We give a procedure to calculate $D(\mathrm{\mid }\vec{p}\mathrm{\mid })$ on available lattices at finite temporal spacing. The result agrees at all momenta with the Gribov formula $D(|\vec{p}|)\propto(|\vec{p}|^2+ M^4 |\vec{p}|^{-2})^{-{1/2}}$,with$M=0.88(1) {\rm GeV} \simeq 2 \sqrt{\sigma}$.