Coulomb-Gauge in QCD: Renormalization and Confinement

We review the Coulomb gauge in QCD and report some recent results. Theminimal Coulomb gauge is defined and the fundamental modular region, a regionwithout Gribov copies, is described. The Coulomb gauge action is expressed interms of the dynamical degrees of freedom with an instantaneous Coulombinteraction, and its physical meaning is discussed. The local Coulomb gaugeaction with phase-space and ghost variables is derived, and its BRS-invarianceand renormalizability are reviewed. It is shown that the instantanteous part$V(R)$ of $g^2 D_{00}(R, t)$, the time-time component of the gluon propagator,is a renormalization-group invariant $V(R) = f(R\Lambda_{QCD})/R$, and that thecontribution of $V(R)$ to the Wilson loop exponentiates. It is conjectured that$V(R) \sim \kappa_{coul}R$ at large $R$, and that $\kappa_{coul}$ provides anorder parameter for confinement of color even in the presence of dynamicalquarks.Comment: 12 pages, 0 figures, Lecture given at the 1997 Yukawa International Seminar at Kyoto, Japa