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We extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is realized as a numerical simulation of the one-asset version. The gauge field background enforces minimal arbitrage, yet allows for statistical fluctuations. The new feature added to the model is an updating prescription for the simulation that drives the model market into a self-organized critical state. Taking advantage of some flexibility of the updating prescription, stylized features and dynamical behaviors of real-world markets are reproduced in some detail., Comment: 19 pages, 11 figures compiled from 33 eps files

We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tuning parameters. Prominent results of our simulation are time series of gains, prices, volatility, and gains frequency distributions, which all compare favorably to features of historical market data. Applying a standard GARCH(1,1) fit to the lattice model gives results that are almost indistinguishable from historical NASDAQ data., Comment: 20 pages, 33 figures

We compute the ground-state energies of a heavy-light K-Lambda like system as a function of the relative distance r of the hadrons. The heavy quarks, one in each hadron, are treated as static. Then, the energies give rise to an adiabatic potential Va(r) which we use to study the structure of the five-quark system. The simulation is based on an anisotropic and asymmetric lattice with Wilson fermions. Energies are extracted from spectral density functions obtained with the maximum entropy method. Our results are meant to give qualitative insight: Using the resulting adiabatic potential in a Schroedinger equation produces bound state wave functions which indicate that the ground state of the five-quark system resembles a hadronic molecule, whereas the first excited state, having a very small rms radius, is probably better described as a five-quark cluster, or a pentaquark. We hypothesize that an all light-quark pentaquark may not exist, but in the heavy-quark sector it might, albeit only as an excited state., Comment: 11 pages, 15 figures, 4 tables

Time correlation functions of a hybrid exotic meson operator, with JPC=1-+, generated in quenched lattice QCD are subjected to a (Bayesian) maximum entropy analysis. Five distinct spectral levels are uncovered. Their extrapolation into the physical pion mass region suggests a possible relationship to experimentally known states pi1(1400) and pi1(1600), and also to a state in the 2 GeV region carrying the same quantum numbers., Comment: 8 pages, 14 eps files, 2 tables, revtex4

A decay width calculation for a hybrid exotic meson h, with JPC=1-+, is presented for the channel h->pi+a1. This quenched lattice QCD simulation employs Luescher's finite box method. Operators coupling to the h and pi+a1 states are used at various levels of smearing and fuzzing, and at four quark masses. Eigenvalues of the corresponding correlation matrices yield energy spectra that determine scattering phase shifts for a discrete set of relative pi+a1 momenta. Although the phase shift data is sparse, fits to a Breit-Wigner model are attempted, resulting in a decay width of about 60 MeV when averaged over two lattice sizes., Comment: 9 pages, 8 figures, RevTex4, minor change to Fig. 1

We present results of a decay width calculation for a hybrid exotic meson(h, JPC=1-+) in the decay channel h to pi+a1. This calculation uses quenched lattice QCD and Luescher's finite box method. Operators for the h and pi+a1 states are used in a correlation matrix which was expanded by varying the smearing and fuzzing levels at source and sink points. Scattering phase shifts for a discrete set of relative pi+a1 momenta are determined using eigenvalues of the correlation matrix and formulae derived by Luescher. The phase shift data is very sparse, but fits to a Breit-Wigner model are made, resulting in a decay width of about 80 MeV., Comment: 8 pages, 5 figures, APS revtex4 documentclass, contribution to Lattice 2005

We study time correlation functions of operators representing heavy-light K-Lambda like systems at various relative distances r. The heavy quarks, one in each hadron, are treated as static. An anisotropic and asymmetric lattice is used with Wilson fermions. Our goal is to extract an adiabatic potential and thus learn about the physics of the five-quark system viewed as an hadronic molecule., Comment: 8 pages, 7 figures, APS revtex4 documentclass, contribution to Lattice 2005

The effective residual interaction for a system of hadrons has a long tradition in theoretical physics. It has been mostly addressed in terms of boson exchange models. The aim of this review is to describe approaches based on lattice field theory and numerical simulation. At the present time this subject matter is in an exploratory stage. A large array of problems waits to be tackled, so that known features of hadron-hadron interactions will eventually be understood in a model-independent way. The lattice formulation, being capable of dealing with the nonperturbative regime, describes strong-interaction physics from first principles, i.e. quantum chromodynamics (QCD). Although the physics of hadron-hadron interactions may be intrinsically complicated, the methods used in lattice simulations are simple: For the most part they are based on standard mass calculations. This chapter addresses commonly used techniques, within QCD and also simpler lattice models, describes important results, and also gives some insight into numerical methods for multi-quark systems., Comment: 89 pages, 49 figures, prepared for World Scientific Publishing Company (International Review of Nuclear Physics, Vol. 9, Hadronic Physics from Lattice QCD, edited by A. M. Green)

We study mass spectra of a meson-meson system involving two light and two heavy quarks on an anisotropic lattice. The heavy quarks are treated in the static approximation. The dependence of the spectrum on the relative distance of the heavy quarks is extracted from the lattice simulation using the maximum entropy method (MEM). A correlation matrix of meson-meson operators emphasizing quark and gluon exchange degrees of freedom is employed in an attempt to learn about aspects of mechanisms of hadronic interaction., Comment: 15 pages, 36 figure files (eps), requires REVTeX 4.0 and prerequisites (AMS-LaTeX 2.0, graphicx, dcolumn, bm) see http://publish.aps.org/revtex4

We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss practical issues of the approach., Comment: 11 pages, 30 figure files (eps), some references added and updated, requires REVTeX 4.0 and prerequisites (AMS-LaTeX 2.0, graphicx, dcolumn, bm) see http://publish.aps.org/revtex4/

A system of two static quarks, at fixed distances r, and two light quarks is studied on an anisotropic lattice. Excitations by operators emphasizing quark or gluon degrees of freedom are examined. The maximum entropy method is applied in the spectral analysis. These simulations ultimately aim at learning about mechanisms of hadronic interaction., Comment: 5 pages, latex (uses espcrc2, psfig), contriubution to: Workshop on Lattice Hadron Physics (LHP2001), Cairns, July 9-18, 2001

A system of two static quarks, at fixed distances r, and two light quarks is studied on an anisotropic lattice. Excitations by operators emphasizing quark or gluon degrees of freedom are examined. The maximum entropy method is applied in the spectral analysis. These simulations ultimately aim at learning about mechanisms of hadronic interaction., Comment: 3 pages, 5 figures, Lattice2001(matrixelement)

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., Comment: LATTICE98(spectrum) LaTeX2e, 3 pages, 3 eps figures

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., Comment: LaTeX2e, 29 pages, 14 eps figures

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., Comment: 3 pages, 5 EPS figures, Poster presented at "Lattice'97", to appear in the proceedings

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., Comment: 3 pages, 4 EPS figures, Poster presented at "Lattice'97", to appear in the proceedings

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., Comment: 4 pages, 6 figures, LaTeX uses espcrc2.sty, to be published in Nucl. Phys. B (Proc. Suppl.), Talk presented at LATTICE96(phenomenology)

Meson and baryon masses in the light (u,d and s) sector are calculated using tadpole-improved gauge field and fermion actions. These are corrected to order $O(a^2)$ on the classical level using next-nearest-neighbour terms. The results, obtained at lattice spacings of 0.4 and 0.27fm, are compared to Wilson action calculations., Comment: Talk presented at LATTICE96(improvement)

Calculations of hadron masses are done in quenched approximation using gauge field and fermion actions which are both corrected for discretization errors to $O(a^2)$ at the classical level and which contain tadpole improvement factors. The fermion action has both nearest-neighbour and next-nearest-neighbour couplings in the kinetic and Wilson terms. Simulations done at lattice spacings of $0.27$ and $0.4$fm yield hadron masses which are already quite close to experimental values. The results are compared to Wilson action calculations done at comparable lattice spacings., Comment: 18 pages, 3 postscript figures, revised May 1996

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., Comment: 4 pages, uuencoded gziped postscript file, contribution to LATTICE'95, Melbourne, Australia (list of authors completed)

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., Comment: 12 pages, uuencoded tar-compressed postscript file

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., Comment: 4 pages, uuencoded tar-compressed postscript file, contribution to Lattice'95

The residual interaction for a meson-meson system is computed utilizing the cumulant, or cluster, expansion of the momentum-space time correlation matrix. The cumulant expansion serves to define asymptotic, or free, meson-meson operators. The definition of an effective interaction is then based on a comparison of the full (interacting) and the free (noninteracting) time correlation matrices. The proposed method, which may straightforwardly be transcribed to other hadron-hadron systems, here is applied to a simple 2+1 dimensional U(1) lattice gauge model tuned such that it is confining. Fermions are treated in the staggered scheme. The effective interaction exhibits a repulsive core and attraction at intermediate relative distances. These findings are consistent with an earlier study of the same model utilizing L\"{u}scher's method where scattering phase shifts are obtained directly., Comment: 28 pages, compressed postscript file

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., Comment: 3 pages, uuencoded tar-compressed postscript file, contribution to Lattice'94, Bielefeld, to be published in Nucl. Phys. B (Proc. Suppl.) 1995, (fiebig@servms.fiu.edu)

Scattering phase shifts of a meson-meson system in staggered 3-dimensional lattice QED are computed. The main task of the simulation is to obtain a discrete set of two-body energy levels. These are extracted from a 4-point time correlation matrix and then used to obtain scattering phase shifts. The results for the l=0 and l=2 partial waves are consistent with short- range repulsion and intermediate-range attraction of the residual meson- meson interaction.