Gauge Fixing and the Gibbs Phenomenon

We address the question of why global gauge fixing, specifically to the lattice Landau gauge, becomes an extremely lengthy process for large lattices. We construct an artificial "gauge-fixing" problem which has the essential features encountered in actuality. In the limit in which the size of the system to be gauge fixed becomes infinite, the problem becomes equivalent to finding a series expansion in functions which are related to the Jacobi polynomials. The series converges slowly, as expected. It also converges non-uniformly, which is an observed characteristic of gauge fixing. In the limiting example, the non-uniformity arises through the Gibbs phenomenon.Comment: 3 Pages; Talk at Lattice '98; Postscript version only - not available in te

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

Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.Comment: talk given by M. M.-P. at the Workshop on Computational Hadron Physics, Cyprus, September 200

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 $D(k)$ and $G(k)$ in Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by $D(k) \sim 1/(k^2)^{1 + a_D}$ and $G(k) \sim 1/(k^2)^{1 + a_G}$ are obtained in space-time dimensions $d = 2, 3, 4$. Two possible solutions are obtained with the values, in $d = 4$ dimensions, $a_G = 1, a_D = -2$, or $a_G = [93 - (1201)^{1/2}]/98 \approx 0.595353, a_D = - 2a_G$.Comment: 26 pages. Modified 2.25.02 to update references and to clarify Introduction and Conclusio

Hyper-Raman scattering from vitreous boron oxide: coherent enhancement of the boson peak

Hyper-Raman scattering spectra of vitreous B$_2$O$_3$ are reported and compared to Raman scattering results. The main features are indexed in terms of vibrations of structural units. Particular attention is given to the low frequency boson peak which is shown to relate to out-of-plane librations of B$_3$O$_3$ boroxol rings and BO$_3$ triangles. Its hyper-Raman strength is comparable to that of cooperative polar modes. It points to a sizeable coherent enhancement of the hyper-Raman signal compared to the Raman one. This is explained by the symmetry of the structural units.Comment: 4 pages, 3 figure

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 $BRS$ symmetry.Comment: 17 pages, NYU-TH-93/10/0

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

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

The gluon and ghost propagator and the influence of Gribov copies

The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU(3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approachComment: Talk presented at Lattice2004(topology), Fermilab, June 21-26, 2004, 3 pages, 3 figure