Monopole Spectra in non-Abelian Gauge Theories

We study the continuum limit of the length spectrum of magnetic monopole structures found after various Abelian projections of pure gauge SU(2), including the maximally Abelian gauge. We comment on Gribov copies, and measurements of the string tension.Comment: Talk presented at LATTICE96(topology) LaTeX, with 4 LaTeX figure

Gribov Copies in the Maximally Abelian Gauge and Confinement

We fix $SU(2)$ lattice gauge fields to the Maximally Abelian gauge in both three and four dimensions. We extract the corresponding $U(1)$ fields and monopole current densities and calculate separately the confining string tensions arising from these $U(1)$ fields and monopole `condensates'. We generate multiple Gribov copies and study how the $U(1)$ fields and monopole distributions vary between these different copies. As expected, we find substantial variations in the number of monopoles, their locations and in the values of the $U(1)$ field strengths. The string tensions extracted from `extreme' Gribov copies also differ but this difference appears to be no more than about 20\%. We also directly compare the fields of different Gribov copies. We find that on the distance scales relevant to confinement the $U(1)$ and monopole fluxes that disorder Wilson loops are highly correlated between these different Gribov copies. All this suggests that while there is indeed a Gribov copy problem the resulting ambiguity is, in this gauge and for the study of confinement, of limited importance.Comment: 31 pages LaTeX plus 5 PostScript figures. Uses epsf.sty. Self-unpacking, uuencoded tar-compressed fil

String Tension from Monopoles in SU(2) Lattice Gauge Theory

The axis for Figure 2 was wrong. It has been fixed and the postscript file replaced (The file was called comp.ps).Comment: (22 pages latex (revtex); 2 figures appended as postscript files - search for mono.ps and comp.ps. Figures mailed on request--send a note to [email protected]) Preprint ILL-(TH)-94-#1

Monopole clusters in Abelian projected gauge theories

We show that the monopole currents which one obtains in the maximally Abelian gauge of SU(2) fall into two quite distinct classes (when the volume is large enough). In each field configuration there is precisely one cluster that permeates the whole lattice volume. It has a current density and a magnetic screening mass that scale and it produces the whole of the string tension. The remaining clusters have a number density that follows an approximate power law proportional to the inverse cube of l where l is the length of the monopole world line in lattice units. These clusters are localised in space-time with radii which vary as the square root of l. In terms of the radius r these `lumps' have a scale-invariant distribution proportional to (dr/r . 1/{r^4}). Moreover they appear not to contribute at all to the string tension. The fact that they are scale-invariant at small distances would seem to rule out an instanton origin.Comment: LaTeX, 31 pages, 11 PostScript figures. Typo in Table 2 correcte

Lattice Gauge Fixing and the Violation of Spectral Positivity

Spectral positivity is known to be violated by some forms of lattice gauge fixing. The most notable example is lattice Landau gauge, where the effective gluon mass is observed to rise rather than fall with increasing distance. We trace this violation to the use of quenched auxiliary fields in the lattice gauge fixing process, and show that violation of spectral positivity is a general feature of quenching. We illustrate this with a simple quenched mass-mixing model in continuum field theory, and with a quenched form of the Ising model. For lattice gauge fixing associated with Abelian projection and lattice Landau gauge, we show that spectral positivity is violated by processes similar to those found in quenched QCD. For covariant gauges parametrized by a gauge-fixing parameter $\alpha$, the SU(2) gluon propagator is well described by a simple quenched mass-mixing formula. The gluon mass parameter appears to be independent of $\alpha$ for sufficiently large $\alpha$.Comment: 8 pages, 6 eps figures, RevTeX4; shortene

EC02-179 Managing Livestock Manure to Protect Environmental Quality

This book covers the land application part of manure management. With increasing regulations, the livestock producer needs to understand the scientific principles that affect manure transformations and how to use these principles to manage the manure for maximum fertilizer value with minimal environmental impact. Improved land application of manure is one part of the solution, but we suggest that the producer evaluate the quantity of nutrients arriving on the farm as feed, animals, and fertilizer compared to the total that is exported. Achieving a nutrient balance will reduce potential environmental hazards often associated with animal agriculture

Dual Superconductor Scenario of Confinement: A Systematic Study of Gribov Copy Effects

We perform a study of the effects from maximal abelian gauge Gribov copies in the context of the dual superconductor scenario of confinement, on the basis of a novel approach for estimation of systematic uncertainties from incomplete gauge fixing. We present numerical results, in SU(2) lattice gauge theory, using the overrelaxed simulated annealing gauge fixing algorithm. We find abelian and non-abelian string tensions to differ significantly, their ratio being 0.92(4) at BETA = 2.5115. An approximate factorization of the abelian potential into monopole and photon contributions has been confirmed, the former giving rise to the abelian string tension.Comment: 35 pages uucompressed LaTeX with 10 encapsuled postscript figure

738–2 The Evolution of Therapy for Single Vessel Disease: A Treatment Comparison of Medicine, Angioplasty and Left Internal Mammary Artery Graft for Proximal Left Anterior Descending Disease

Saphenous vein bypass grafting for single vessel disease offers no survival or symptom relief advantage compared to medical therapy. Recent evidence suggests the use of the internal mammary artery or PTCA may be more beneficial than medicine. To examine the outcome of these treatment strategies, a retrospective analysis of prospectively collected data on 23,018 consecutive patients undergoing cardiac catheterization between April 1986 and February 1994 was performed. Of the 6,432 patients with single vessel disease, 1,222 had a proximal left anterior descending (LAD) stenosis>74% and no prior PTCA or CABG. A total of 289 were managed medically, 760 underwent PTCA, and 172 received a left internal mammary artery (LIMA) graft.Baseline demographic data and risk factor profiles were similar except for a higher incidence of diabetes (19 vs 15 vs 11%), history of MI (72 vs 58 vs 48%) CHF (18 vs 7 vs 8%), and total occlusions (44 vs 17 vs 7%) and lower incidence of unstable angina (40 vs 61 vs 64%) in the medical group as compared to PTCA and LIMA graft, respectively.Kaplan-Meier 6-year estimates:EventsMedicinePTCALIMAP-value–unadjusted survival (%)7885910.001–adjusted survival (%)8486900.24–event-free survival (%)5443720.0001ConclusionThere is a trend towards improved long-term survival in proximal LAD disease with a strategy of revascularization, particularly the LIMA graft. Furthermore, event-free survival is significantly improved with the LIMA graft as compared to medical therapy or PTCA

Observing Long Colour Flux Tubes in SU(2) Lattice Gauge Theory

We present results of a high statistics study of the chromo field distribution between static quarks in SU(2) gauge theory on lattices of volumes 16^4, 32^4, and 48^3*64, with physical extent ranging from 1.3 fm up to 2.7 fm at beta=2.5, beta=2.635, and beta=2.74. We establish string formation over physical distances as large as 2 fm. The results are tested against Michael's sum rules. A detailed investigation of the transverse action and energy flux tube profiles is provided. As a by-product, we obtain the static lattice potential in unpreceded accuracy.Comment: 66 pages, 29 figures, uuencoded latex file with epsfigures (450 K), supplementary full colour figures are available via ftp, CERN-TH.7413/94 (extended version

Free energy of an SU(2) monopole-antimonopole pair

We present a high-statistic numerical study of the free energy of a monopole-antimonopole pair in pure SU(2) theory. We find that the monopole-antimonopole interaction potential exhibits a screened behavior, as one would expect in presence of a monopole condensate. Screening occurs both in the low-temperature, confining phase of the theory, and in the high-temperature deconfined phase, with no evidence of a discontinuity of the screening mass across the transition. The mass of the object responsible for the screening at low temperature is approximately twice the established value for the lightest glueball, indicating a prevalent coupling to glueball excitations. At high temperature, the screening mass increases. We contrast the behavior of the quantum system with that of the corresponding classical system, where the monopole-antimonopole potential is of the Coulomb type.Comment: Latex, 22 pages, 8 figures. A mistake in the computer program implementing the multihistogram method has been corrected and all the affected numerical data have been revised. The main conclusions of the paper are unchanged, but the screening masses turn out somehow larger. (We thank Philippe de Forcrand for correspondence which helped us find the error.