arXiv subjects

H. Markum

Publications and source records attributed to H. Markum.

At least 37 records · Page 2Linked to original sources

arXiv1998

Action and topological density carried by Abelian monopoles in finite temperature pure SU(2) gauge theory: an analysis using RG smoothing

We test a new parametrization of a suitably truncated classically perfect action for SU(2) pure gauge theory with respect to self-consistency and locate the deconfinement transition on a 12^3X4 lattice. Using the technique of smoothing (blocking followed by inverse blocking) we demonstrate clustering of action and topological charge density. Concentrating on the Abelian monopoles found in smoothed configurations after Abelian projection from the maximally Abelian gauge, we present evidence for their role as carriers of non-Abelian action and topological charge.

hep-lat↗

arXiv1998

Towards a Topological Mechanism of Quark Confinement

We report on new analyses of the topological and chiral vacuum structure of four-dimensional QCD on the lattice. Correlation functions as well as visualization of monopole currents in the maximally Abelian gauge emphasize their topological origin and gauge invariant characterization. The (anti)selfdual character of strong vacuum fluctuations is reveiled by smoothing. In full QCD, (anti)instanton positions are also centers of the local chiral condensate and quark charge density. Most results turn out generically independent of the action and the cooling/smoothing method.

hep-lat↗

arXiv1998

Evidence for quantum chaos in the plasma phase of QCD

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD on a $6^3\times 4$ lattice. As a measure of the fluctuation properties of the eigenvalues, we study the nearest-neighbor spacing distribution $P(s)$ for various values of $β$ both in the confinement and in the deconfinement phase. In both phases except far into the deconfinement region, the lattice data agree with the Wigner surmise of random-matrix theory which is indicative of quantum chaos. We do not find signs of a transition to Poisson regularity at the deconfinement phase transition.

hep-ph↗

arXiv1997

Two-body spectra of pseudoscalar mesons with an $O(a^2)$--improved lattice action using Wilson fermions

We extend our calculations with the second-order tree-level and tadpole improved next-nearest-neighbor action to meson-meson systems. Correlation matrices built from interpolating fields representing two pseudoscalar mesons (pion-pion) with relative momenta p are diagonalized, and the mass spectrum is extracted. Link variable fuzzing and operator smearing at both sinks and sources is employed. Calculations are presented for two values of the hopping parameter. The spectrum is used to discuss the residual interaction in the meson-meson system.

hep-lat↗

arXiv1997

Potentials between heavy-light mesons from lattice and inverse scattering theory

We extend our investigation of heavy-light meson-meson interactions to a system consisting of a heavy-light meson and the corresponding antiparticle. An effective potential is obtained from meson-antimeson Green-functions computed in a quenched simulation with staggered fermions. Comparisons with a simulation using an $O(a^2)$ tree-level and tadpole improved gauge action and a full QCD simulation show that lattice discretization errors and dynamical quarks have no drastic influence. Calculations from inverse scattering theory propose a similar shape for $K\bar{K}$ potentials.

hep-lat↗

arXiv1997

Topology without cooling: instantons and monopoles near to deconfinement

In an attempt to describe the change of topological structure of pure SU(2) gauge theory near deconfinement a renormalization group inspired method is tested. Instead of cooling, blocking and subsequent inverse blocking is applied to Monte Carlo configurations to capture topological features at a well-defined scale. We check that this procedure largely conserves long range physics like string tension. UV fluctuations and lattice artefacts are removed which otherwise spoil topological charge density and Abelian monopole currents. We report the behaviour of topological susceptibility and monopole current densities across the deconfinement transition and relate the two faces of topology to each other. First results of a cluster analysis are described.

hep-lat↗

arXiv1997

Quantum chaos in QCD at finite temperature

We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the nearest-neighbor spacing distribution $P(s)$ for various values of $β$ both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.

hep-lat↗

arXiv1997

Coexistence of monopoles and instantons for different topological charge definitions and lattice actions

We compute instanton sizes and study correlation functions between instantons and monopoles in maximum abelian projection within SU(2) lattice QCD at finite temperature. We compare several definitions of the topological charge, different lattice actions and methods of reducing quantum fluctuations. The average instanton size turns out to be $σ\approx 0.2$ fm. The correlation length between monopoles and instantons is $ζ\approx 0.25$ fm and hardly affected by lattice artifacts as dislocations. We visualize several specific gauge field configurations and show directly that there is an enhanced probability for finding monopole loops in the vicinity of instantons. This feature is independent of the topological charge definition used.

hep-lat↗

arXiv1997

Instantons and monopoles in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This feature is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover we investigate how monopole loops and instantons are correlated with the chiral condensate. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.

hep-lat↗

arXiv1996

Forces between composite particles in QCD

Starting from the meson-meson Green function in 3+1 dimensional quenched lattice QCD we calculate potentials between heavy-light mesons for various light-quark mass parameters. For the valence quarks we employ the staggered scheme. The resulting potentials turn out to be short ranged and attractive. A comparison with a tadpole improved action for the gauge fields is presented.

hep-lat↗

arXiv1996

Correlation functions in lattice formulations of quantum gravity

We compare different models of a quantum theory of four-dimensional lattice gravity based on Regge's original proposal. From Monte Carlo simulations we calculate two-point functions between geometrical quantities and estimate the masses of the corresponding interaction particles.

hep-lat↗

arXiv1996

Correlation functions between topological objects -- field theoretic versus geometric definitions

We analyze topological objects in pure gluonic $SU(2)$ lattice gauge theory and compute correlation functions between instantons and monopoles. Concerning the instantons we use geometric and field theoretic definitions of the topological charge. On a $12^3\times 4$ lattice it turns out that topological quantities have a non-trivial local correlation. The auto-correlation functions of the topological charge depend on cooling for both definitions. We fit the correlation functions to exponentials and obtain screening masses.

hep-lat↗

arXiv1996

Visualization of topological objects in QCD

Recently evidence appeared that instantons and monopoles have a certain local correlation in four-dimensional pure $SU(2)$ and $SU(3)$ gauge theory. We visualize several specific gauge field configurations and show directly that there is an enhanced probability for finding maximally projected abelian monopole loops in the vicinity of instantons. This feature is independent of the topological charge definition used.

hep-lat↗

arXiv1996

Relations Between Monopoles, Instantons and Chiral Condensate

We analyze the interplay of topological objects in four dimensional QCD. The distributions of color magnetic monopoles obtained in the maximum abelian gauge are computed around instantons in both pure and full QCD. We find an enhanced probability of encountering monopoles inside the core of an instanton on gauge field average. For specific gauge field configurations we visualize the situation graphically. Moreover we investigate how monopole loops and instantons are locally correlated with the chiral condensate.

hep-lat↗

arXiv1996

Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times 2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the $β$-function of pure gauge theory and conclude that a physical limit through scaling is possible.

hep-lat↗

arXiv1995

Meson-meson interactions -- from static to dynamic valence quarks

A method for the extraction of an effective meson-meson potential from Green functions, which can be obtained from a lattice simulation, is presented. Simulations are carried out for compact QED and QCD in four dimensions using the quenched approximation and the hopping parameter expansion. In a further study, a heavy-light meson is considered employing a conjugate gradient algorithm for the light propagators. Due to the Pauli exclusion principle, the results for QED indicate the existence of a hard core, but for QCD there is strong attraction at small meson distances.

hep-lat↗

arXiv1995

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.

hep-lat↗

arXiv1995

The phase structure of pure Regge gravity

We examine the phase structure of pure Regge gravity in four dimensions and compare our Monte Carlo results with $Z_2$-link Regge-theory as well as with another formulation of lattice gravity derived from group theoretical considerations. Within all three models we find an extension of the well-defined phase to negative gravitational coupling and a new phase transition. In contrast to the well-known transition at positive coupling there is evidence for a continuous phase transition which might be essential for a possible continuum limit.

hep-lat↗