299 research outputs found
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
Nonperturbative contributions to the QCD pressure
We summarize the most important arguments why a perturbative description of
finite-temperature QCD is unlikely to be possible and review various
well-established approaches to deal with this problem. Then, using a recently
proposed method, we investigate nonperturbative contributions to the QCD
pressure and other observables (like energy, anomaly and bulk viscosity)
obtained by imposing a functional cutoff at the Gribov horizon. Finally, we
discuss how such contributions fit into the picture of consecutive effective
theories, as proposed by Braaten and Nieto, and give an outline of the next
steps necessary to improve this type of calculation.Comment: 15 pages, 13 figures, uses xcolor.sty; in v2 quality of some figures
has been improved, discussion of other approaches has been extende
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
Soft Covariant Gauges on the Lattice
We present an exploratory study of a one-parameter family of covariant,
non-perturbative lattice gauge-fixing conditions, that can be implemented
through a simple Monte Carlo algorithm. We demonstrate that at the numerical
level the procedure is feasible, and as a first application we examine the
gauge dependence of the gluon propagator.Comment: 11 pages, Latex, epsf.sty included + 5 PostScript picture
Residual internal stress in partially crystallized photothermorefractive glass: Evaluation by nuclear magnetic resonance spectroscopy and first principles calculations
In some circumstances, the mechanical and optical properties of multiphase brittle materials strongly depend on the level of residual micromechanical stresses that arise upon cooling due to thermal and elastic mismatch between the constituent phases. Here we study the residual internal stress in a partially crystallized oxyfluoride glass, best known as photothermorefractive (PTR) glass. This material is composed of a glass matrix with embedded nanosize sodium fluoride (NaF) crystals. Using both the Selsing model and solid-state nuclear magnetic resonance in combination with first principles calculations we found that the crystals are under a tensile stress field of approximately 610-800 MPa. For this stress level the estimated critical crystal diameter for spontaneous cracking is about 2300-1900 nm, which greatly exceeds the observed diameters of 7-35 nm. Hence no spontaneous cracking is expected for the PTR glasses. First principles calculations indicate that the stress induced change of the refractive index of the NaF crystals is about -0.08%, which agrees with the observed refractive index changes
On practical problems to compute the ghost propagator in SU(2) lattice gauge theory
In SU(2) lattice pure gauge theory we study numerically the dependence of the
ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau)
gauge. We find that the effect of Gribov copies is essential in the scaling
window region, however, it tends to decrease with increasing beta. On the other
hand, we find that at larger beta-values very strong fluctuations appear which
can make problematic the calculation of the ghost propagator.Comment: 15 pages, 5 postscript figures. 2 Figures added Revised version as to
be published in Phys.Rev.
The Gribov horizon and the one-loop color-Coulomb potential
We recalculate the color-Coulomb potential to one-loop order, under the
assumption that the effect of the Gribov horizon is to make i) the transverse
gluon propagator less singular; and ii) the color-Coulomb potential more
singular, than their perturbative behavior in the low-momentum limit. As a
first guess, the effect of the Gribov horizon is mimicked by introducing a
transverse momentum-dependent gluon mass term, leading to a propagator of the
Gribov form, with the prescription that the mass parameter should be adjusted
to the unique value where the infrared behavior of the Coulomb potential is
enhanced. We find that this procedure leads to a Coulomb potential rising
asymptotically as a linear term modified by a logarithm.Comment: 15 pages, 2 figure
SU(2) Landau gluon propagator on a 140^3 lattice
We present a numerical study of the gluon propagator in lattice Landau gauge
for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2,
5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V
we observe a decreasing gluon propagator for momenta smaller than p_{dec} =
350^{+ 100}_{- 50} MeV. Data are well fitted by Gribov-like formulae and seem
to indicate an infra-red critical exponent kappa slightly above 0.6, in
agreement with recent analytic results.Comment: 5 pages with 2 figures and 3 tables; added a paragraph on
discretization effect
Inhomogeneous phase of a Gluon Plasma at finite temperature and density
By considering the non-perturbative effects associated with the fundamental
modular region, a new phase of a Gluon Plasma at finite density is proposed. It
corresponds to the transition from glueballs to non-perturbative gluons which
condense at a non vanishing momentum. In this respect the proposed phase is
analogous to the color superconducting LOFF phase for fermionic systems.Comment: 5 pages, 2 figure
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