Monopoles and Chaos

We decompose U(1) gauge fields into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. It turns out that there is a strong relation between the sizes of the monopole density and the Lyapunov exponent.Comment: Contribution to HEP-MAD'01 - High-Energy Physics International Conferences (Antananarivo, Madagascar, 2001/09/27 - 2001/10/05), 6 pages, 5 figure

Chirality tubes along monopole trajectories

We classify the lattice by elementary 3-cubes which are associated to dual links occupied by, or free of monopoles. We then compute the quark condensate, the quark charge and the chiral density on those cubes. By looking at distributions we demonstrate that monopole trajectories carry considerably more chirality with respect to the free vacuum.Comment: LATTICE99(topology), 3 pages, eps figure

Chiral condensate, quark charge and chiral density

We study the topological and fermionic vacuum structure of four-dimensional QCD on the lattice by means of correlators of fermionic observables and topological densities. We show the existence of strong local correlations between the topological charge density and the quark condensate, charge and chiral density. By analysis of individual gauge configurations, we visualize that instantons (antiinstantons) carry positive (negative) chirality, whereas the quark charge density fluctuates in sign within instantons.Comment: LATTICE98(confine), 3 pages, 2 figure

Lyapunov exponents in Minkowskian U(1) gauge theory

U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular.Comment: Lattice2002(topology), 3 pages, 4 figure

Monopole density around static color sources

We analyze the vacuum structure with respect to magnetic monopoles of quenched QCD in the presence of static color sources. Distributions of the monopole density around static quarks and mesons are computed in both phases of QCD. We observe a suppression of the monopole density in the vicinity of external sources. In the confinement phase the density of color magnetic monopoles is reduced along the flux tube between a static quark-antiquark pair.Comment: 3 pages, uuencoded postscriptfile (690kB), Contribution to the XII INTERNATIONAL SYMPOSIUM ON LATTICE FIELD THEORY, Bielefeld, Germany, 199

Observables of Lattice Gauge Theory in Minkowski Space

U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. Evidence is found that monopole fields stay chaotic in the continuum whereas the photon fields are regular. First results are presented for the full spectrum of Lyapunov exponents of the U(1) gauge system.Comment: Contribution to "QCD02 - High-Energy Physics International Conference in Quantum Chromodynamics" (Montpellier, France, July 02 - 09, 2002); 5 pages, 9 figure

Topological charge density around static colour sources in lattice QCD with dynamical quarks

We update our numerical investigation of topological structures around static quarks in pure gauge QCD by results of the first runs including dynamical quarks. Simulations were performed on an $8^3\times4$ lattice, with $SU(3)$ Wilson action, with 3 flavours of quarks of equal mass, both in the confinement and deconfinement phase. In the confinement phase we observe indications for the existence of a flux tube between a static quark and antiquark, flux-tube breaking for large separations, and local correlation between the topological charge density and chiral condensate. In the deconfinement phase almost all configurations turn out to be topologically trivial.Comment: 3 pages, PostScript, uuencoded and compressed tar file (Contribution to LATTICE 94 in Bielefeld.

Correlation functions between monopoles and instantons

We analyze the relation between instantons and abelian projected monopoles in both phases of pure QCD by calculating local correlation functions between topological charge densities and monopole densities. On an $8^{3} \times 4$ lattice, it turns out that topological quantities are correlated approximately two lattice spacings. The monopole-instanton correlations are rather insensitive under cooling of gauge fields.Comment: 4 pages, uuencoded gziped postscript file, contribution to LATTICE'95, Melbourne, Australi

Zero-modes of the QED Neuberger Dirac operator

We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.Comment: Lattice2001(confinement), 6 pages, 9 figure