41,661 research outputs found
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
Numerical Study of Gluon Propagator and Confinement Scenario in Minimal Coulomb Gauge
We present numerical results in SU(2) lattice gauge theory for the
space-space and time-time components of the gluon propagator at equal time in
the minimal Coulomb gauge. It is found that the equal-time would-be physical
3-dimensionally transverse gluon propagator vanishes at
when extrapolated to infinite lattice volume, whereas the
instantaneous color-Coulomb potential is strongly enhanced at
. This has a natural interpretation in a confinement scenario in
which the would-be physical gluons leave the physical spectrum while the
long-range Coulomb force confines color. Gribov's formula provides an excellent fit to our data
for the 3-dimensionally transverse equal-time gluon propagator
for relevant values of .Comment: 23 pages, 12 figures, TeX file. Minor modifications, incorporating
referee's suggestion
Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge
The infrared behavior of the gluon propagator is directly related to
confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement
predicts an infrared vanishing (transverse) gluon propagator in Landau-like
gauges, implying violation of reflection positivity and gluon confinement.
Finite-volume effects make it very difficult to observe (in the minimal Landau
gauge) an infrared suppressed gluon propagator in lattice simulations of the
four-dimensional case. Here we report results for the SU(2) gluon propagator in
a gauge that interpolates between the minimal Landau gauge (for gauge parameter
lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0).
For small values of lambda we find that the spatially-transverse gluon
propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta
|\vec p|, is clearly infrared suppressed. This result is in agreement with the
Gribov-Zwanziger scenario and with previous numerical results in the minimal
Coulomb gauge. We also discuss the nature of the limit lambda -> 0 (complete
Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our
findings are corroborated by similar results in the three-dimensional case,
where the infrared suppression is observed for all considered values of lambda.Comment: 5 pages, 2 figures, one figure with additional results and extended
discussion of some aspects of the results added and some minor
clarifications. In v3: Various small changes and addition
Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips
We determine the general structure of the partition function of the -state
Potts model in an external magnetic field, for arbitrary ,
temperature variable , and magnetic field variable , on cyclic, M\"obius,
and free strip graphs of the square (sq), triangular (tri), and honeycomb
(hc) lattices with width and arbitrarily great length . For the
cyclic case we prove that the partition function has the form ,
where denotes the lattice type, are specified
polynomials of degree in , is the corresponding
transfer matrix, and () for ,
respectively. An analogous formula is given for M\"obius strips, while only
appears for free strips. We exhibit a method for
calculating for arbitrary and give illustrative
examples. Explicit results for arbitrary are presented for
with and . We find very simple formulas
for the determinant . We also give results for
self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W
The Tensor Current Divergence Equation in U(1) Gauge Theories is Free of Anomalies
The possible anomaly of the tensor current divergence equation in U(1) gauge
theories is calculated by means of perturbative method. It is found that the
tensor current divergence equation is free of anomalies.Comment: Revtex4, 7 pages, 2 figure
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