arXiv subjects

Michael Engelhardt

Publications and source records attributed to Michael Engelhardt.

72 records · Page 4Linked to original sources

arXiv2004

Generation of confinement and other nonperturbative effects by infrared gluonic degrees of freedom

Recent progress in understanding the emergence of confinement and other nonperturbative effects in the strong interaction vacuum is reviewed. Special emphasis is placed on the role of different types of collective infrared gluonic degrees of freedom in this respect. After a survey of complementary approaches, models of the QCD vacuum based on center vortices, Abelian magnetic monopoles and topological charge lumps such as instantons, merons and calorons are examined. Both the physical mechanisms governing these models as well as recent lattice studies of the respective degrees of freedom are reviewed.

hep-lat↗

arXiv2004

Educational Content Management - A Cellular Approach

In recent times online educational applications more and more are requested to provide self-consistent learning offers for students at the university level. Consequently they need to cope with the wide range of complexity and interrelations university course teaching brings along. An urgent need to overcome simplistically linked HTMLc ontent pages becomes apparent. In the present paper we discuss a schematic concept of educational content construction from information cells and introduce its implementation on the storage and runtime layer. Starting from cells content is annotated according to didactic needs, structured for dynamic arrangement, dynamically decorated with hyperlinks and, as all works are based on XML, open to any presentation layer. Data can be variably accessed through URIs built on semantic path-names and edited via an adaptive authoring toolbox. Our content management approach is based on the more general Multimedia Information Repository MIR. and allows for personalisation, as well. MIR is an open system supporting the standards XML, Corba and JNDI.

cs.CY↗

arXiv2004

Semantic Linking - a Context-Based Approach to Interactivity in Hypermedia

The semantic Web initiates new, high level access schemes to online content and applications. One area of superior need for a redefined content exploration is given by on-line educational applications and their concepts of interactivity in the framework of open hypermedia systems. In the present paper we discuss aspects and opportunities of gaining interactivity schemes from semantic notions of components. A transition from standard educational annotation to semantic statements of hyperlinks is discussed. Further on we introduce the concept of semantic link contexts as an approach to manage a coherent rhetoric of linking. A practical implementation is introduced, as well. Our semantic hyperlink implementation is based on the more general Multimedia Information Repository MIR, an open hypermedia system supporting the standards XML, Corba and JNDI.

cs.IR↗

arXiv2004

Hypermedia Learning Objects System - On the Way to a Semantic Educational Web

While eLearning systems become more and more popular in daily education, available applications lack opportunities to structure, annotate and manage their contents in a high-level fashion. General efforts to improve these deficits are taken by initiatives to define rich meta data sets and a semanticWeb layer. In the present paper we introduce Hylos, an online learning system. Hylos is based on a cellular eLearning Object (ELO) information model encapsulating meta data conforming to the LOM standard. Content management is provisioned on this semantic meta data level and allows for variable, dynamically adaptable access structures. Context aware multifunctional links permit a systematic navigation depending on the learners and didactic needs, thereby exploring the capabilities of the semantic web. Hylos is built upon the more general Multimedia Information Repository (MIR) and the MIR adaptive context linking environment (MIRaCLE), its linking extension. MIR is an open system supporting the standards XML, Corba and JNDI. Hylos benefits from manageable information structures, sophisticated access logic and high-level authoring tools like the ELO editor responsible for the semi-manual creation of meta data and WYSIWYG like content editing.

cs.IR↗

arXiv2004

Center vortex model for the infrared sector of SU(3) Yang-Mills theory -- baryonic potential

The baryonic potential in the framework of the SU(3) random vortex world-surface model is evaluated for a variety of static color source geometries. For comparison, carefully taking into consideration the string tension anisotropy engendered by the hypercubic lattice description, also the Delta and Y law predictions for the baryonic potential are given. Only the Y law predictions are consistent with the baryonic potentials measured.

hep-lat↗

arXiv2003

Writhe of center vortices and topological charge -- an explicit example

The manner in which continuum center vortices generate topological charge density is elucidated using an explicit example. The example vortex world-surface contains one lone self-intersection point, which contributes a quantum 1/2 to the topological charge. On the other hand, the surface in question is orientable and thus must carry global topological charge zero due to general arguments. Therefore, there must be another contribution, coming from vortex writhe. The latter is known for the lattice analogue of the example vortex considered, where it is quite intuitive. For the vortex in the continuum, including the limit of an infinitely thin vortex, a careful analysis is performed and it is shown how the contribution to the topological charge induced by writhe is distributed over the vortex surface.

hep-th↗

arXiv2002

Center vortex model for the infrared sector of Yang-Mills theory - Quenched Dirac spectrum and chiral condensate

The Dirac operator describing the coupling of continuum quark fields to SU(2) center vortex world-surfaces composed of elementary squares on a hypercubic lattice is constructed. It is used to evaluate the quenched Dirac spectral density in the random vortex world-surface model, which previously has been shown to quantitatively reproduce both the confinement properties and the topological susceptibility of SU(2) Yang-Mills theory. Under certain conditions on the modeling of the vortex gauge field, a behavior of the quenched chiral condensate as a function of temperature is obtained which is consistent with measurements in SU(2) lattice Yang-Mills theory.

hep-lat↗

arXiv2002

Center vortex model for nonperturbative strong interaction physics

A model for the infrared sector of SU(2) Yang-Mills theory, based on magnetic vortex degrees of freedom represented by (closed) random world-surfaces, is presented. The model quantitatively describes both the confinement properties (including the finite-temperature transition to a deconfined phase) and the topological susceptibility of the Yang-Mills ensemble. A (quenched) study of the spectrum of the Dirac operator furthermore yields a behavior for the chiral condensate which is compatible with results obtained in lattice gauge theory.

hep-lat↗

arXiv2001

Susceptibility of Monte-Carlo Generated Projected Vortices

We determine the topological susceptibility from center projected vortices and demonstrate that the topological properties of the SU(2) Yang-Mills vacuum can be extracted from the vortex content. We eliminate spurious ultraviolet fluctuations by two different smoothing procedures. The extracted susceptibility is comparable to that obtained from full field configurations.

hep-lat↗

arXiv2001

On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.

hep-th↗

arXiv2000

Center vortex model for the infrared sector of Yang-Mills theory - Topological Susceptibility

A definition of the Pontryagin index for SU(2) center vortex world-surfaces composed of plaquettes on a hypercubic lattice is constructed. It is used to evaluate the topological susceptibility in a previously defined random surface model for vortices, the parameters of which have been fixed such as to reproduce the confinement properties of SU(2) Yang-Mills theory. A prediction for the topological susceptibility is obtained which is compatible with measurements of this quantity in lattice Yang-Mills theory.

hep-lat↗

arXiv1997

Effective potential for the order parameter of the SU(2) Yang-Mills deconfinement transition

The Polyakov loop variable serves as an order parameter to characterize the confined and deconfined phases of Yang-Mills theory. By integrating out the vector fields in the SU(2) Yang-Mills partition function in one-loop approximation, an effective action is obtained for the Polyakov loop to second order in a derivative expansion. The resulting effective potential for the Polyakov loop is capable of describing a second-order deconfinement transition as a function of temperature.

hep-th↗

arXiv1997

One-dimensional classical adjoint SU(2) Coulomb Gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.

hep-th↗

arXiv1996

Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational approach for matrix models. Approximate variational solutions of interacting large-N matrix models are found using the free random matrices as the variational space. Several classes of classical and quantum mechanical matrix models with different types of interactions are considered and the variational solutions compared with exact Monte Carlo and analytical results. Impressive agreement is found in a majority of cases.

hep-th↗

arXiv1996

Nonrelativistic Particle in Free Random Gauge Background

The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature connected with noncommuting random variables. In the context of large-N hermitian matrices, it means that the the multi-matrix model considered contains no bias with respect to the relative orientations of the matrices. In such a gauge background, the spectrum of a colored particle can be solved for analytically. In three dimensions, near zero momentum, the energy distribution for the spinless particle displays a gap, while the energy distribution for the particle with spin does not.

hep-th↗

arXiv1995

On Eigenvalue Decompactification in QCD$_{1+1} $

The question whether it is necessary to decompactify the gauge eigenvalue degrees of freedom in QCD$_{1+1} $ is addressed. A careful consideration of the dynamics governing these degrees of freedom leads to the conclusion that eigenvalue decompactification is not necessary due to the curvature on the space of eigenvalues.

hep-th↗

arXiv1995

Finite-Sized Plasmas

When addressing the thermodynamics of finite-sized systems, one must specify whether one wants to fix conserved charges to a sharp value or whether one is content to fix their thermodynamic average. In other words, contrary to the thermodynamic limit, different statistical ensembles are not equivalent. When treating the plasma phases of gauge field theories perturbatively in the canonical ensemble, unexpected new difficulties arise in comparison with the usual grand canonical treatment. The purpose of this paper is to expose these difficulties and show how they can be remedied, thus recovering a well-defined description of plasmas even in a finite-size, canonical ensemble setting. For definiteness, a specific model is considered, namely QCD$_{1+1} $ with SU(2) color; however, the treatment presented should be applicable also to higher-dimensional systems with different types of Coulomb interaction.

hep-ph↗

arXiv1994

QCD_{1+1} at large N_F and N_C

QCD in 1+1 dimensions is examined in the limit of a large number of colors and flavors. The Hamiltonian matrix is given in a Fock space spanned by 't Hooft meson states and, for the case of zero fermion mass, a submatrix is diagonalized numerically to give the low-lying spectrum as a function of $N_F /N_C $. Pair creation effects generate bound states which are complicated mixtures of components of different meson number. There are a number of nontrivial zero modes; in the massive part of the spectrum some states tend to a well-defined $N_F \gg N_C $ limit while others become unstable and disappear. The masses of most states remain remarkably constant over a large range of $N_F /N_C $.

hep-ph↗