ar X iv : h ep - l at / 0 11 01 89 v 1 2 2 O ct 2 00 1 1 Confinement made simple in the Coulomb gauge ∗

In Gribov’s scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V (R). This may be determined numerically from the instantaneous part of the gluon propagator D44,inst = V (R)δ(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three-dimensionally transverse would-be physical gluon propagator D(k). We present exact analytic results on D44 and D tr (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of D(k) at k = 0, and the determination of the running coupling constant from x0g (k) = k2D44,inst, where x0 = 12N/(11N − 2Nf ).