arXiv subjects

H. Markum

Publications and source records attributed to H. Markum.

At least 55 records · Page 3Linked to original sources

arXiv1995

Extraction of hadron-hadron potentials on the lattice within 2+1 dimensional QED

A potential between mesons is extracted from 4-point functions within lattice gauge theory taking 2+1 dimensional QED as an example. This theory possesses confinement and dynamical fermions. The resulting meson-meson potential has a short-ranged hard repulsive core due to antisymmetrization. The expected dipole-dipole forces lead to attraction at intermediate distances. Sea quarks lead to a softer form of the total potential.

hep-lat↗

arXiv1995

On the nature of the residual meson-meson interaction from simulations with a QED${}_{2+1}$ model

A potential between mesons is extracted from 4-point functions within lattice gauge theory taking 2+1 dimensional QED as an example. This theory possesses confinement and dynamical fermions. The resulting meson-meson potential has a short-ranged hard repulsive core and the expected dipole-dipole forces lead to attraction at intermediate distances. Sea quarks lead to a softer form of the total potential.

hep-lat↗

arXiv1995

Correlations between Quarks, Monopoles and Instantons

We analyze topological objects in pure QCD in the presence of external quarks by calculating the distributions of instanton and monopole densities around static color sources. We find a suppression of the densities close to external sources and the formation of a flux tube between a static quark--antiquark pair. The similarity in the behavior of instantons and monopoles around static sources might be due to a local correlation between these topological objects. On an $8^{3} \times 4$ lattice at $β=5.6$, it turns out that topological quantities are correlated approximately two lattice spacings.

hep-th↗

arXiv1995

Effective meson-meson interaction in 2+1 dimensional lattice QED

A definition of an effective meson-meson interaction adapted to the framework of a lattice simulation is presented. Results, based on a truncated momentum-space 4-point time correlation matrix, and preliminary data from a complementary coordinate-space simulation, are shown.

hep-lat↗

arXiv1995

Static Quark Potentials in Quantum Gravity

We present potentials between static charges from simulations of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. The action consists of the gravitational term given by Regge's discrete version of the Euclidean Einstein action and a gauge term given by the Wilson action, with coupling constants $m_{p}^{2}$ and $β$ respectively. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. We compare potentials on a flat simplicial lattice with those on a fluctuating Regge skeleton. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.

hep-lat↗

arXiv1994

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.

hep-lat↗

arXiv1994

Quantum gravity and spin systems

A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations considerably. In two dimensions equivalence to an Ising model with ternary couplings is recovered. First simulations in four dimensions indicate strong similarities to the phase structure of original Regge theory.

hep-lat↗

arXiv1994

SU(2) potentials in quantum gravity

We present investigations of the potential between static charges from a simulation of quantum gravity coupled to an SU(2) gauge field on $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. In the well-defined phase of the gravity sector where geometrical expectation values are stable, we study the correlations of Polyakov loops and extract the corresponding potentials between a source and sink separated by a distance $R$. In the confined phase, the potential has a linear form while in the deconfined phase, a screened Coulombic behavior is found. Our results indicate that quantum gravitational effects do not destroy confinement due to non-abelian gauge fields.

hep-lat↗

arXiv1994

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.

hep-lat↗

arXiv1994

Flux tubes and topological charges in finite-temperature lattice QCD

Topological properties of the vacuum were investigated in finite-temperature lattice QCD without and with dynamical quarks using a local operator of topological charge density and a variant of cooling. Below the deconfinement temperature evidence for flux tube formation was observed in the distribution of topological charge density around a static $Q\bar Q$ pair. With dynamical quarks, the flux tube breaks when the distance between the static quark and antiquark increases.

hep-lat↗

arXiv1994

The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions

We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy dominated phase with small negative curvature is investigated in detail. It turns out that observables of the system possess finite expectation values although the Einstein-Hilbert action is unbounded. This well-defined phase is found to be stable for a one-parameter family of measures. A preliminary study indicates that the influence of the lattice size on the average curvature is small. We compare our results with those obtained by dynamical triangulation and find qualitative correspondence.

hep-lat↗

arXiv1993

Gluon Versus Meson Exchange in Hadron-Hadron Systems on the Lattice

The interaction of spatially extended heavy hadrons is investigated in the framework of lattice QCD with dynamical quarks. In addition to the baryon-baryon potential results for the baryon-antibaryon and for the meson-meson system are presented. It is shown that the expected dipole forces have a very short range and that sea quarks play a minor important role.

hep-lat↗

arXiv1993

Baryon-Baryon Potentials on the Lattice

The interaction of spatially extended heavy baryons is investigated in the framework of lattice QCD with dynamical quarks. It is shown that the expected dipole forces have a very short range and that the baryon-antibaryon interaction is more attractive than the baryon-baryon interaction. Sea quarks play a minor important role.

hep-lat↗

arXiv1993

Two-Point Functions of Four-Dimensional Simplicial Quantum Gravity

We investigate the interaction mechanism of pure quantum gravity in Regge discretization. We compute volume-volume and link-link correlation functions. In a preliminary analysis the forces turn out to be of Yukawa type, at least on our finite lattice being away from the continuum limit.

hep-lat↗

arXiv1993

Two-Dimensional Lattice Gravity as a Spin System

Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagome lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.

hep-lat↗

arXiv1993

On the Measure of Simplicial Quantum Gravity in Four Dimensions

We study quantum gravity in the path-integral formulation using the Regge calculus. In spite of the unbounded gravitational action the existence of an entropy-dominated phase is confirmed. The influence of various types of measures on this phase structure is investigated and our results are compared with those obtained by dynamical triangulation.

hep-lat↗

arXiv1992

Gravitational Action Versus Entropy on Simplicial Lattices in Four Dimensions

We investigate quantum gravity on simplicial lattices using Regge calculus with special emphasize on the problem of the unbounded action. The role of the entropy for the path integral is discussed in detail. Our numerical results show further evidence for the existence of an entropy dominated region with well defined expectation values even for unbounded action. Analyses are performed both for the standard regular triangulation of the 4-torus and for irregularly triangulated lattices obtained by insertion of vertices using barycentric subdivision.

hep-lat↗

arXiv1992

Quantum-Gravity Path-Integrals on Simplicial Lattices

Euclidean quantum-gravity path-integrals are investigated within Regge calculus by computer simulations. The domain of integration is restricted by introducing a lower limit for the fatness of each simplex. We use the standard hypercubic triangulation of the 4-torus and irregularly triangulated lattices obtained by inserting a small number of vertices using barycentric subdivision. For limited fatness we find an entropy dominated phase with small negative curvature both for the regular and the irregular triangulation.

hep-lat↗