Numerical Study of the Gluon Propagator in Lattice Landau Gauge: the Three-Dimensional Case

We study the infrared behavior of the gluon propagator in lattice Landau gauge, for pure SU(2) lattice gauge theory in a three-dimensional lattice. Simulations are done for nine different values of the coupling $\beta$, from $\beta = 0$ (strong coupling) to $\beta = 6.0$ (in the weak-coupling region). In the limit of large lattice volumes, we observe in all cases a gluon propagator decreasing as the momentum goes to zero.Comment: LATTICE98(confine

Effects of Nonperturbative Improvement in Quenched Hadron Spectroscopy

We discuss a comparative analysis of unimproved and nonperturbatively improved quenched hadron spectroscopy, on a set of 104 gauge configurations, at beta=6.2. We also present here our results for meson decay constants, including the constants f_D and f_Ds in the charm-quark region.Comment: LATTICE98(spectrum

SU(2) lattice gluon propagators at finite temperatures in the deep infrared region and Gribov copy effects

We study numerically the SU(2) Landau gauge transverse and longitudinal gluon propagators at non-zero temperatures T both in confinement and deconfinement phases. The special attention is paid to the Gribov copy effects in the IR-region. Applying powerful gauge fixing algorithm we find that the Gribov copy effects for the transverse propagator D_T(p) are very strong in the infrared, while the longitudinal propagator D_L(p) shows very weak (if any) Gribov copy dependence. The value D_T(0) tends to decrease with growing lattice size; however, D_T(0) is non-zero in the infinite volume limit, in disagreement with the suggestion made in [1]. We show that in the infrared region D_T(p) is not consistent with the pole-type formula not only in the deconfinement phase but also for T < T_c. We introduce new definition of the magnetic infrared mass scale ('magnetic screening mass') m_M. The electric mass m_E has been determined from the momentum space longitudinal gluon propagator. We study also the (finite) volume and temperature dependence of the propagators as well as discretization errors.Comment: 11 pages, 14 figures, 3 tables. Few minor change

Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian

The static color-Coulomb potential is calculated as the solution of a non-linear integral equation. This equation has been derived recently as a self-consistency condition which arises in the Coulomb Hamiltonian formulation of lattice gauge theory when the restriction to the interior of the Gribov horizon is implemented. The potential obtained is in qualitative agreement with expectations, being Coulombic with logarithmic corrections at short range and confining at long range. The values obtained for the string tension and $\Lambda_{\overline{MS}}$ are in semi-quantitative agreement with lattice Monte Carlo and phenomenological determinations.Comment: 4 pages (including 1 figure); (latex using espcrc2.sty). Talk presented at LATTICE96(poster

Confinement made simple in the Coulomb gauge

In Gribov's scenario in Coulomb gauge, confinement of color charge is due to a long-range instantaneous color-Coulomb potential V(R). This may be determined numerically from the instantaneous part of the gluon propagator D_{44, inst} = V(R) \delta(t). Confinement of gluons is reflected in the vanishing at k = 0 of the equal-time three-dimensionally transverse would-be physical gluon propagator D^{tr}(k). We present exact analytic results on D_{44} and D^{tr} (which have also been investigated numerically, A. Cucchieri, T. Mendes, and D. Zwanziger, this conference), in particular the vanishing of D^{tr}(k) at k = 0, and the determination of the running coupling constant from x_0 g^2(k) = k^2 D_{44, inst}, where x_0 = 12N/(11N-2N_f).Comment: 3 pages; talk presented by D. Zwanziger at Lattice2001(confinement), Berlin, August 20-24, 200

How to extract information from Green's functions in Landau gauge

The infrared behavior of gluon and ghost propagators offers a crucial test of confinement scenarios in Yang-Mills theories. A nonperturbative study of these propagators from first principles is possible in lattice simulations, but one must consider significantly large lattice sizes in order to approach the infrared limit. We propose constraints based on general properties of the propagators to gain control over the extrapolation of data to the infinite-volume limit. These bounds also provide a way to relate the propagators to simpler, more intuitive quantities. We apply our analysis to the case of pure SU(2) gauge theory in Landau gauge, using the largest lattice sizes to date. Our results seem to contradict commonly accepted confinement scenarios. We argue that it is not so.Comment: 6 pages, proceedings of SPMTP08 (Dubna, June 2008), talk presented by A. Cucchier