1,159 research outputs found
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
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
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
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