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

Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory

We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color-Coulomb potential at large distances is governed by the near-zero FP eigenmodes; in particular, the lowest one accounts for a substantial portion of the color-Coulomb string tension comparable to the Wilson string tension.Comment: 14 pages, 14 figure

Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields

The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.Comment: talk given by H. Reinhardt on the Int. Workshop ``Hadrons 1999'', Coimbra, 10.-15. Sept. 199

Coulomb gauge gluon propagator and the Gribov formula

We analyze the lattice SU(2) Yang-Mills theory in Coulomb gauge. We show that the static gluon propagator is multiplicative renormalizable and takes the simple form $D(|\vec{p}|)^{-1}=\sqrt{|\vec{p}|^2+M^4/|\vec{p}|^2}$, proposed by Gribov through heuristic arguments many years ago. We find $M=0.88(1) {\rm GeV} \simeq 2 \sqrt{\sigma}$.Comment: 10 pages, 2 figures. Slight change of notations, some point clarified. To appear on Phys. Rev. Let

Fermion Energies in the Background of a Cosmic String

We provide a thorough exposition, including technical and numerical details, of previously published results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. We combine the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. We show that strings carrying fermion charge become stable if the electro-weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in our model, because neutral strings are not energetically favored. These findings suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.Comment: 38 pages, 6 figures, version accepted for publication in Phys Rev

Magnetic Monopoles, Center Vortices and Topology of Gauge Fields

The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed.Comment: talk presented at LATTICE99(topology) at Pisa, Italy, 3 page

A general solution in the Newtonian limit of f(R)- gravity

We show that any analytic $f(R)$-gravity model, in the metric approach, presents a weak field limit where the standard Newtonian potential is corrected by a Yukawa-like term. This general result has never been pointed out but often derived for some particular theories. This means that only $f(R)=R$ allows to recover the standard Newton potential while this is not the case for other relativistic theories of gravity. Some considerations on the physical consequences of such a general solution are addressed.Comment: 5 page