On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.Comment: 24 pages, 4 eps-figures; new version matches published on

The role of center vortices in Gribov's confinement scenario

The connection of Gribov's confinement scenario in Coulomb gauge with the center vortex picture of confinement is investigated. For this purpose we assume a vacuum wave functional which models the infrared properties of the theory and in particular shows strict confinement, i.e. an area law of the Wilson loop. We isolate the center vortex content of this wave functional by standard lattice methods and investigate their contributions to various static propagators of the Hamilton approach to Yang-Mills theory in Coulomb gauge. We find that the infrared properties of these quantities, in particular the infrared divergence of the ghost form factor, are dominated by center vortices.Comment: 18 pages, 5 figure

Ghost propagator and the Coulomb form factor from the lattice

We calculate the Coulomb ghost propagator G(|p|) and the static Coulomb potential V_C(|r|) for SU(2) Yang-Mills theory on the lattice. In view of possible scaling violations related to deviations from the Hamiltonian limit we use anisotropic lattices to improve the temporal resolution. We find that the ghost propagator is infrared enhanced with an exponent kappa_gh ~ 0.5 while the Coulomb potential exhibits a string tension larger than the Wilson string tension, sigma_C ~ 2 sigma. This agrees with the Coulomb "scaling" scenario derived from the Gribov-Zwanziger confinement mechanism.Comment: 23 pages, 5 figures. Some issues clarified and extended, references added. To appear in PR