Propagators in Coulomb gauge from SU(2) lattice gauge theory

A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is performed using large scale lattice simulations. The (equal-time) transverse gluon propagator, the ghost form factor d(p) and the Coulomb potential V-coul(p)proportional tod(2)(p)f(p)/p(2) are calculated. For large momenta p, the gluon propagator decreases like 1/p(1+eta) with eta=0.5(1). At low momentum, the propagator is weakly momentum dependent. The small momentum behavior of the Coulomb potential is consistent with linear confinement. We find that the inequality sigma(coul)greater than or equal tosigma is satisfied. Finally, we provide evidence that the ghost form factors d(p) and f(p) acquire IR singularities, i.e., d(p)proportional to1/rootp and f(p)proportional to1/p, respectively. It turns out that the combination g(0)(2)d(0)(p) of the bare gauge coupling g(0) and the bare ghost form factor d(0)(p) is finite and therefore renormalization group invariant.