426 research outputs found
Renormalization-group Calculation of Color-Coulomb Potential
We report here on the application of the perturbative renormalization-group
to the Coulomb gauge in QCD. We use it to determine the high-momentum
asymptotic form of the instantaneous color-Coulomb potential and
of the vacuum polarization . These quantities are
renormalization-group invariants, in the sense that they are independent of the
renormalization scheme. A scheme-independent definition of the running coupling
constant is provided by , and of , where , and
is a finite QCD mass scale. We also show how to calculate the
coefficients in the expansion of the invariant -function , where all coefficients are scheme-independent.Comment: 24 pages, 1 figure, TeX file. Minor modifications, incorporating
referee's suggestion
Properties of Color-Coulomb String Tension
We study the properties of the color-Coulomb string tension obtained from the
instantaneous part of gluon propagators in Coulomb gauge using quenched SU(3)
lattice simulation.
In the confinement phase, the dependence of the color-Coulomb string tension
on the QCD coupling constant is smaller than that of the Wilson loop string
tension. On the other hand, in the deconfinement phase, the color-Coulomb
string tension does not vanish even for , the temperature
dependence of which is comparable with the magnetic scaling, dominating the
high temperature QCD. Thus, the color-Coulomb string tension is not an order
parameter of QGP phase transition.Comment: 17 pages, 5 figures; one new figure added, typos corrected, version
to appear in PR
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
Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories
We show that the confining property of the one-gluon propagator, in Coulomb
gauge, is linked to the unbroken realization of a remnant gauge symmetry which
exists in this gauge. An order parameter for the remnant gauge symmetry is
introduced, and its behavior is investigated in a variety of models via
numerical simulations. We find that the color-Coulomb potential, associated
with the gluon propagator, grows linearly with distance both in the confined
and - surprisingly - in the high-temperature deconfined phase of pure
Yang-Mills theory. We also find a remnant symmetry-breaking transition in SU(2)
gauge-Higgs theory which completely isolates the Higgs from the
(pseudo)confinement region of the phase diagram. This transition exists despite
the absence, pointed out long ago by Fradkin and Shenker, of a genuine
thermodynamic phase transition separating the two regions.Comment: 18 pages, 19 figures, revtex
Non-perturbative Landau gauge and infrared critical exponents in QCD
We discuss Faddeev-Popov quantization at the non-perturbative level and show
that Gribov's prescription of cutting off the functional integral at the Gribov
horizon does not change the Schwinger-Dyson equations, but rather resolves an
ambiguity in the solution of these equations. We note that Gribov's
prescription is not exact, and we therefore turn to the method of stochastic
quantization in its time-independent formulation, and recall the proof that it
is correct at the non-perturbative level. The non-perturbative Landau gauge is
derived as a limiting case, and it is found that it yields the Faddeev-Popov
method in Landau gauge with a cut-off at the Gribov horizon, plus a novel term
that corrects for over-counting of Gribov copies inside the Gribov horizon.
Non-perturbative but truncated coupled Schwinger-Dyson equations for the gluon
and ghost propagators and in Landau gauge are solved
asymptotically in the infrared region. The infrared critical exponents or
anomalous dimensions, defined by and are obtained in space-time dimensions . Two
possible solutions are obtained with the values, in dimensions, , or .Comment: 26 pages. Modified 2.25.02 to update references and to clarify
Introduction and Conclusio
Landau gauge within the Gribov horizon
We consider a model which effectively restricts the functional integral of
Yang--Mills theories to the fundamental modular region. Using algebraic
arguments, we prove that this theory has the same divergences as ordinary Yang
Mills theory in the Landau gauge and that it is unitary. The restriction of the
functional integral is interpreted as a kind of spontaneous breakdown of the
symmetry.Comment: 17 pages, NYU-TH-93/10/0
Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
The non-perturbative domain of QCD contains confinement, chiral symmetry
breaking, and the bound state spectrum. For the calculation of the latter, the
Coulomb gauge is particularly well-suited. Access to these non-perturbative
properties should be possible by means of the Green's functions. However,
Coulomb gauge is also very involved, and thus hard to tackle. We introduce a
novel BRST-type operator r, and show that the left-hand side of Gauss' law is
r-exact.
We investigate a possible truncation scheme of the Dyson-Schwinger equations
in first-order formalism for the propagators based on an instantaneous
approximation. We demonstrate that this is insufficient to obtain solutions
with the expected property of a linear-rising Coulomb potential. We also show
systematically that a class of possible vertex dressings does not change this
result.Comment: 22 pages, 4 figures, 1 tabl
Heat-kernel expansion and counterterms of the Faddeev-Popov determinant in Coulomb and Landau gauge
The Faddeev-Popov determinant of Landau gauge in d dimensions and Coulomb
gauge in d+1 dimensions is calculated in the heat-kernel expansion up to
next-to-leading order. The UV-divergent parts in d=3,4 are isolated and the
counterterms required for a non-perturbative treatment of the Faddeev-Popov
determinant are determined.Comment: 7 page
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