arXiv subjects

H. Markum

Publications and source records attributed to H. Markum.

At least 19 recordsLinked to original sources

arXiv2010

Proceedings to the 13th Workshop 'What Comes Beyond the Standard Models', Bled, July 12. - 22., 2010, Slovenia

1. Noncommutativity and Topology within Lattice Field Theories 2. The Construction of Quantum Field Operators 3. The Bargmann-Wigner Formalism for Spin 2 Fields 4. New Light on Dark Matter from the LHC 5. Extra Dimensional Metric Reversal Symmetry and its Prospect... 6. Masses and Mixing Matrices of Families within SU(3) Flavor Symmetry ... 7. Dark Atoms of the Universe: OHe Nuclear Physics, 8. Can the Matter-Antimatter Asymmetry be Easier to Understand Within the "Spin-charge-family-theory", .. 9. Mass Matrices of Twice Four Families of Quarks and Leptons, ...in the "Spin-charge-family-theory" 10. Bohmian Quantum Mechanics or What Comes Before the Standard Model 11. Backward Causation in Complex Action Model ... 12. Is the Prediction of the "Spin-charge-family-theory" in Disagreement with the XENON100..? 13. Masses and Mixing Matrices of Families of Quarks and Leptons Within the "Spin-charge-family-theory" 14. Can the Stable Fifth Family of the "Spin-charge-family-theory" ...Form the Fifth Antibaryon Clusters with Ordinary He Nucleus? 15. Puzzles of Dark Matter - More Light on Dark Atoms? 16. Families of Spinors in d = (1 + 5)...and Masslessness 17. Are Superheavy Quark Clusters Candidates for the Dark Matter? 18. Complex Action Functioning as Cutoff and De Broglie-Bohm Particle 19. Where does the Science Go? 20. VIA Presentation

hep-ph↗

arXiv2003

Discretization and Continuum Limit of Quantum Gravity on a Four-Dimensional Space-Time Lattice

The Regge Calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The Discrete Regge Model limits the choice of the link lengths to a finite number. We examine the phase structure of Standard Regge Calculus in four dimensions and compare our Monte Carlo results with those of the $Z_2$-Regge Model as well as with another formulation of lattice gravity derived from group theoretical considerations. Within all of the three models of quantum gravity we find an extension of the well-defined phase to negative gravitational couplings and a new phase transition. We calculate two-point functions between geometrical quantities at the corresponding critical point and estimate the masses of the respective interaction particles. A main concern in lattice field theories is the existence of a continuum limit which requires the existence of a continuous phase transition. The recently conjectured second-order transition of the four-dimensional Regge skeleton at negative gravity coupling could be such a candidate. We examine this regime with Monte Carlo simulations and critically discuss its behavior.

hep-lat↗

arXiv2003

Concerning the quark condensate

A continuum expression for the trace of the massive dressed-quark propagator is used to explicate a connection between the infrared limit of the QCD Dirac operator's spectrum and the quark condensate appearing in the operator product expansion, and the connection is verified via comparison with a lattice-QCD simulation. The pseudoscalar vacuum polarisation provides a good approximation to the condensate over a larger range of current-quark masses.

nucl-th↗

arXiv2002

Ising spins coupled to a four-dimensional discrete Regge skeleton

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.

hep-lat↗

arXiv2000

Spectrum of the U(1) staggered Dirac operator in four dimensions

We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.

hep-lat↗

arXiv2000

Universality and Chaos in Quantum Field Theories

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution, $P(s)$. We further study two-color QCD at nonzero chemical potential, $μ$, by constructing the spacing distribution of adjacent eigenvalues in the complex plane. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior.

hep-lat↗

arXiv1999

Exploring the pi+ pi+ interaction in lattice QCD

An effective residual interaction for a meson-meson system is computed in lattice QCD. We describe the theoretical framework and present its application to the I=2 channel S-wave interaction of the pi pi system. Scattering phase shifts are also computed and compared to experimental results.

hep-lat↗

arXiv1999

Distribution of fermionic and topological observables on the lattice

We analyze 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 and monopole density on the one side and the quark condensate, charge and chiral density on the other side. Visualization of individual gauge configurations demonstrates that instantons (antiinstantons) carry positive (negative) chirality, whereas the quark charge density fluctuates in sign within instantons.

hep-lat↗

arXiv1999

Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential

In quantum chromodynamics (QCD) at nonzero chemical potential, the eigenvalues of the Dirac operator are scattered in the complex plane. Can the fluctuation properties of the Dirac spectrum be described by universal predictions of non-Hermitian random matrix theory? We introduce an unfolding procedure for complex eigenvalues and apply it to data from lattice QCD at finite chemical potential $μ$ to construct the nearest-neighbor spacing distribution of adjacent eigenvalues in the complex plane. For intermediate values of $μ$, we find agreement with predictions of the Ginibre ensemble of random matrix theory, both in the confinement and in the deconfinement phase.

hep-lat↗

arXiv1999

On the I=2 channel pi-pi interaction in the chiral limit

An approximate local potential for the residual pi+ pi+ interaction is computed. We use an O(a**2) improved action on a coarse 9x9x9x13 lattice with approximately a=0.4fm. The results present a continuation of previous work: Increasing the number of gauge configurations and quark propagators we attempt extrapolation of the pi+ pi+ potential to the chiral limit.

hep-lat↗

arXiv1999

Monopole characteristics in various Abelian gauges

Renormalization group (RG) smoothing is employed on the lattice to investigate and to compare the monopole structure of the SU(2) vacuum as seen in different gauges (maximally Abelian (MAG), Polyakov loop (PG) and Laplacian gauge (LG)). Physically relevant types of monopoles (LG and MAG) are distinguished by their behavior near the deconfining phase transition. For the LG, Abelian projection reproduces well the gauge independent monopole structure encoded in an auxiliary Higgs field. Density and localization properties of monopoles, their non-Abelian action and topological charge are studied. Results are presented confirming the Abelian dominance with respect to the non-perturbative static potential for all gauges considered.

hep-lat↗

arXiv1999

Z_2-Regge versus Standard Regge Calculus in two dimensions

We consider two versions of quantum Regge calculus. The Standard Regge Calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z_2-Regge Model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z_2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z_2-Regge Model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z_2-Regge Model is analyzed by mean-field theory.

hep-lat↗

arXiv1998

Quantum Chaos in Compact Lattice QED

Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.

hep-lat↗

arXiv1998

Gauge invariant properties of Abelian monopoles

Using a renormalization group motivated smoothing technique, we investigate the large scale structure of lattice configurations at finite temperature, concentrating on Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Monopoles are mostly found in regions of large action and topological charge, rather independent of the gauge chosen to detect them. Gauge invariant properties around Abelian monopoles, the local non-Abelian action and topological density, are studied. We show that the local averages of these densities along the monopole trajectories are clearly above the background, which supports the existence of monopoles as physical objects. Characteristic changes of the vacuum structure at the deconfinement transition can be attributed to the corresponding Abelian monopoles, to an extent that depends on the gauge chosen for Abelian projection. All three Abelian projections reproduce the full SU(2) string tension within 10 percent which is preserved by smoothing.

hep-lat↗

arXiv1998

Abelian monopoles in finite temperature lattice gauge fields: Classically perfect action, smoothing and various Abelian gauges

Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian Abelian, and the Polyakov gauge. Abundance and anisotropy of monopoles at deconfinement and gauge invariant properties like local non-Abelian action and topological density are studied. Monopoles are predominantly found in regions of large action and topological charge, rather independent of the chosen gauge.

hep-lat↗

arXiv1998

2d quantum gravity with discrete edge lengths

An approximation of the Standard Regge Calculus (SRC) was proposed by the $Z_2$-Regge Model ($Z_2$RM). There the edge lengths of the simplicial complexes are restricted to only two possible values, both always compatible with the triangle inequalities. To examine the effect of discrete edge lengths, we define two models to describe the transition from the $Z_2$RM to the SRC. These models allow to choose the number of possible link lengths to be $n = {4,8,16,32,64,...}$ and differ mainly in the scaling of the quadratic link lengths. The first extension, the $X^1_n$-Model, keeps the edge lengths limited and still behaves rather similar to the "spin-like" $Z_2$RM. The vanishing critical cosmological constant is reproduced by the second extension, the $X^C_n$-Model, which allows for increasing edge lengths. In addition the area expectation values are consistent with the scaling relation of the SRC.

hep-lat↗

arXiv1998

Quantum chaos and QCD at finite chemical potential

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $μ$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex. We discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(3) simulation with staggered fermions are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $μ\approx 0.7$.

hep-lat↗

arXiv1998

Lattice Models of Quantum Gravity

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+εσ$, with $σ=\pm 1$, in close analogy to the ancestor of all lattice theories, the Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.

hep-lat↗