A Ginzburg-Landau Analysis of the Colour Electric Flux Tube

In a simulation of SU(2) gauge theory we investigate, after maximal Abelian projection, the dual Maxwell equations for colour field and monopole current distributions around a static quark-antiquark pair Q_ Q in vacuo. Within the dual superconductor picture we carry out a Ginzburg-Landau type analysis of the flux tube profile. As a result we can determine the coherence length of the GL wave function related to the monopole condensate, xi = .25(3) fm, to be compared to the penetration length, lambda = >.15(2) fm (scaled with the string tension).Comment: 3 pages, 5 figures, corrected typos, LATTICE98(confine

Quark zero modes in intersecting center vortex gauge fields

The zero modes of the Dirac operator in the background of center vortex gauge field configurations in $\R^2$ and $\R^4$ are examined. If the net flux in D=2 is larger than 1 we obtain normalizable zero modes which are mainly localized at the vortices. In D=4 quasi-normalizable zero modes exist for intersecting flat vortex sheets with the Pontryagin index equal to 2. These zero modes are mainly localized at the vortex intersection points, which carry a topological charge of $\pm 1/2$. To circumvent the problem of normalizability the space-time manifold is chosen to be the (compact) torus \T^2 and \T^4, respectively. According to the index theorem there are normalizable zero modes on \T^2 if the net flux is non-zero. These zero modes are localized at the vortices. On \T^4 zero modes exist for a non-vanishing Pontryagin index. As in $\R^4$ these zero modes are localized at the vortex intersection points.Comment: 20 pages, 4 figures, LaTeX2e, references added, treatment of ideal vortices on the torus shortene

Four-dimensional pure compact U(1) gauge theory on a spherical lattice

We investigate the confinement-Coulomb phase transition in the four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The action contains the Wilson coupling beta and the double charge coupling gamma. The lattice is obtained from the 4D surface of the 5D cubic lattice by its radial projection onto a 4D sphere, and made homogeneous by means of appropriate weight factors for individual plaquette contributions to the action. On such lattices the two-state signal, impeding the studies of this theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a consistent finite-size scaling behavior of several bulk observables is found, with the correlation length exponent nu in the range nu = 0.35 - 40. These observables include Fisher zeros, specific-heat and cumulant extrema as well as pseudocritical values of beta at fixed gamma. The most reliable determination of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at gamma le 0 is thus very probably of 2nd order and belongs to the universality class of a non-Gaussian fixed point.Comment: 40 pages, LaTeX, 12 figure

Enzymatic oligomerization and polymerization of arylamines: state of the art and perspectives

The literature concerning the oxidative oligomerization and polymerization of various arylamines, e.g., aniline, substituted anilines, aminonaphthalene and its derivatives, catalyzed by oxidoreductases, such as laccases and peroxidases, in aqueous, organic, and mixed aqueous organic monophasic or biphasic media, is reviewed. An overview of template-free as well as template-assisted enzymatic syntheses of oligomers and polymers of arylamines is given. Special attention is paid to mechanistic aspects of these biocatalytic processes. Because of the nontoxicity of oxidoreductases and their high catalytic efficiency, as well as high selectivity of enzymatic oligomerizations/polymerizations under mild conditions-using mainly water as a solvent and often resulting in minimal byproduct formation-enzymatic oligomerizations and polymerizations of arylamines are environmentally friendly and significantly contribute to a "green'' chemistry of conducting and redox-active oligomers and polymers. Current and potential future applications of enzymatic polymerization processes and enzymatically synthesized oligo/polyarylamines are discussed

Υ\Upsilon(9.46 GeV) and the gluon discovery (a critical recollection of PLUTO results)

The hadronic decays of Y(9.46GeV) were first studied by PLUTO experiment at DORIS e+e- storage ring (DESY). To determine the contribution of PLUTO to the discovery of the gluon, as members of the collaboration, we have reconsidered all the material produced by it in 1978 and the first half of 1979. It results clearly that the experiment demonstrated the main decay of the Y resonance to be mediated by 3 gluons hadronizing into 3 jets. Jettiness resulted evident by the with respect to the thrust axis, which was as observed by PLUTO itself at nearby continuum c.m.s. energies for 2-quark jet events. Instead, the average sphericity , more topological variables and the momentum distribution showed a net difference with the same data, results compatible with jettiness only in case of more than 2 jets. Flatness as consequence of a 3-body decay (therefore 3 jets) was indicated by the low , altogether a result independent of models. The charged multiplicity was observed to be larger than in the continuum and in case of MC 3 gluon jets fragmenting like quarks, as expected for gluon jets. In June 1979 PLUTO measured the matrix element of the 3-gluon decay to be quantitatively according QCD (even after hadronization, which does not obscure the perturbative predictions) and demonstrated the spin 1 nature of the gluon by excluding spin 0 and spin 1/2. The gluon hadronization like a quark jet, as in 3-gluon jet MC, was compatible with topological data and multiplicity; this was the first experimental study of (identified) gluon jets. The PLUTO results were confirmed both by other experiments at DORIS and later by more sophisticated detectors. At higher energies at PETRA the existence of gluons of spin 1 was confirmed by PLUTO and by 3 more experiments by measuring the gluon radiation, soft gluons by jet broadening, hard gluons by the emission of (now clearly visible) gluon jets by quarks.Comment: 41 pages, 18 figures, substantially revised version of DESY report 10-130, published 21. Oct. 2011 in "The European Physical Journal H (Perspectives on Contemporary Physics)". The final published version is available at http//:www.epj.org. The final author's corrected version is available at arXiv:1008.1869v3 [hep-ex], 18. Nov. 201

On the discovery of the gluon

Quantum chromodynamics, the theory of the strong interaction, is a field theory of quarks and gluons. When it was formulated, the existence of its basic ingredients was still unproven and controversial. While for the quarks the case had been settled by 1975, it remained open for the gluons until in 1979 experiments at the electron-positron collider PETRA at DESY in Hamburg led to a breakthrough. Peculiar final configurations of hadrons produced in the electron-positron annihilation process at high energies, so-called planar events and three-jet events, were discovered. In a close cooperation between experiment and theory they were unambiguously identified as signatures of the radiation of hard gluons by quarks (“hard gluon bremsstrahlung”), providing the first clear and direct observational evidence for the existence of the gluon and confirming crucial predictions of quantum chromodynamics