Instantaneous dynamics of QCD

We start from the observation that, in the confining phase of QCD, the instantaneous color-Coulomb potential in Coulomb gauge is confining. This suggests that, in the confining phase, the dynamics, as expressed in the set of Schwinger-Dyson equations, may be dominated by the purely instantaneous terms. We develop a calculational scheme that expresses the instantaneous dynamics in the local formulation of QCD that includes a cut-off at the Gribov horizon. We get a local, renormalizable quantum field theory with the following interesting properties: -) It provides a cut-off at the Gribov horizon; -) The Kugo-Ojima color confinement condition is satisfied; -) The vacuum is a perfect dielectric; -) The Maggiore-Schaden shift provides a BRST-invariant Lagrangian; -) BRST-symmetry is spontaneously broken, but perhaps only in the unphysical sector; -) In Coulomb gauge, the color-Coulomb potential rises linearly or super-linearly when the Wilson potential is linearly rising; And -) in the instantaneous Schwinger-Dyson equations (ISDE), all loops consist of one instantaneous propagator and the equal-time part of a non-instantaneous propagator