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Monte Carlo simulations of lattice gauge theories

Description: Monte Carlo simulations done for four-dimensional lattice gauge systems are described, where the gauge group is one of the following: U(1); SU(2); Z/sub N/, i.e., the subgroup of U(1) consisting of the elements e 2..pi..in/N with integer n and N; the eight-element group of quaternions, Q; the 24- and 48-element subgroups of SU(2), denoted by T and O, which reduce to the rotation groups of the tetrahedron and the octahedron when their centers Z/sub 2/, are factored out. All of these groups can be considered subgroups of SU(2) and a common normalization was used for the action. The following types of Monte Carlo experiments are considered: simulations of a thermal cycle, where the temperature of the system is varied slightly every few Monte Carlo iterations and the internal energy is measured; mixed-phase runs, where several Monte Carlo iterations are done at a few temperatures near a phase transition starting with a lattice which is half ordered and half disordered; measurements of averages of Wilson factors for loops of different shape. 5 figures, 1 table. (RWR)
Date: February 1, 1980
Creator: Rebbi, C
Partner: UNT Libraries Government Documents Department

Introduction to lattice gauge theory

Description: The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/..cap alpha.., where ..cap alpha.. is the lattice spacing. The continuum (physical) behavior is recovered in the limit ..cap alpha.. ..-->.. 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs.
Date: January 1, 1987
Creator: Gupta, R.
Partner: UNT Libraries Government Documents Department

Lattice overview

Description: After reviewing some recent developments in supercomputer access, the author discusses a few areas where perturbation theory and lattice gauge simulations make contact. The author concludes with a brief discussion of a deterministic dynamics for the Ising model. This may be useful for numerical studies of nonequilibrium phenomena. 13 references.
Date: January 1, 1984
Creator: Creutz, M.
Partner: UNT Libraries Government Documents Department

Research in theoretical physics

Description: This report discusses: hamiltonian lattice gauge theory; relativistic potential model; chiral potential models; covariant dynamical chiral symmetry breaking models of hadronic structure; light-cone calculations and models; and strangeness in the nucleon. LSP
Date: January 1, 1991
Creator: Robson, D. & Williams, A.G.
Partner: UNT Libraries Government Documents Department

Elementary particle physics and high energy phenomena. [Dept. of Physics, Univ. of Colorado, Boulder, Colorado]

Description: Experimental and theoretical high-energy physics programs at the University of Colorado are reported. Areas of concentration include the following: study of the properties of the Z[sup 0] with the SLD detector; fixed-target K-decay experiments; the R D program for the muon system: the SDC detector; high-energy photoproduction of states containing heavy quarks; electron--positron physics with the CLEO II detector at CESR; lattice QCD; and spin models and dynamically triangulated random surfaces. 24 figs., 2 tabs., 117 refs.
Date: June 1, 1992
Creator: Barker, A.R.; Cumalat, J.P.; De Alwis, S.P.; DeGrand, T.A.; Ford, W.T.; Mahanthappa, K.T. et al.
Partner: UNT Libraries Government Documents Department

Novel nuclear phenomena in quantum chromodynamics

Description: Many of the key issues in understanding quantum chromodynamics involve processes in nuclear targets at intermediate energies. A range of hadronic and nuclear phenomena-exclusive processes, color transparency, hidden color degrees of freedom in nuclei, reduced nuclear amplitudes, jet coalescence, formation zone effects, hadron helicity selection rules, spin correlations, higher twist effects, and nuclear diffraction were discussed as tools for probing hadron structure and the propagation of quark and gluon jets in nuclei. Several areas were also reviewed where there has been significant theoretical progress determining the form of hadron and nuclear wave functions, including QCD sum rules, lattice gauge theory, and discretized light-cone quantization. A possible interpretation was also discussed of the large spin correlation A/sub NN/ in proton-proton scattering, and how relate this effect to an energy and angular dependence of color transparency in nuclei. 76 refs., 24 figs.
Date: August 1, 1987
Creator: Brodsky, S.J.
Partner: UNT Libraries Government Documents Department

Energy sciences supercomputing 1990

Description: This report contains papers on the following topics: meeting the computational challenge; lattice gauge theory: probing the standard model; supercomputing for the superconducting super collider; and overview of ongoing studies in climate model diagnosis and intercomparison; MHD simulation of the fueling of a tokamak fusion reactor through the injection of compact toroids; gyrokinetic particle simulation of tokamak plasmas; analyzing chaos: a visual essay in nonlinear dynamics; supercomputing and research in theoretical chemistry; monte carlo simulations of light nuclei; parallel processing; and scientists of the future: learning by doing.
Date: January 1, 1990
Creator: Mirin, A.A. & Kaiper, G.V. (eds.)
Partner: UNT Libraries Government Documents Department

Statistical mechanics and field theory. [Path integrals, lattices, pseudofree vertex model]

Description: Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references.
Date: May 1, 1979
Creator: Samuel, S.A.
Partner: UNT Libraries Government Documents Department

Nuclear physics at extreme energy density

Description: This report discusses topics in the following areas: QCD transport theory; minijets in hadronic and nuclear collisions; lattice gauge theory; hadronic matter and other studies; and strong electromagnetic fields. (LSP)
Date: May 15, 1992
Creator: Mueller, B.
Partner: UNT Libraries Government Documents Department

Food for thought: Five lectures on lattice gauge theory

Description: The topics covered in these lectures are the heavy anti qq potential, glueballs, the chiral transition with dynamical fermions, Weak interaction matrix elements on the lattice and Monte Carlo renormalization group. Even though for the most part these lectures are reviews, many new results and ideas are also presented. The emphasis is on critical analysis of existing data, exposing bottlenecks and a discussion of open problems. Five individual papers have been indexed separately.
Date: January 1, 1987
Creator: Gupta, R.
Partner: UNT Libraries Government Documents Department

Topics in Statistical Mechanics

Description: This thesis deals with four independent topics in statistical mechanics: (1) the dimer problem is solved exactly for a hexagonal lattice with general boundary using a known generating function from the theory of partitions. It is shown that the leading term in the entropy depends on the shape of the boundary; (2) continuum models of percolation and self-avoiding walks are introduced with the property that their series expansions are sums over linear graphs with intrinsic combinatorial weights and explicit dimension dependence; (3) a constrained SOS model is used to describe the edge of a simple cubic crystal. Low and high temperature results are derived as well as the detailed behavior near the crystal facet; (4) the microscopic model of the lambda-transition involving atomic permutation cycles is reexamined. In particular, a new derivation of the two-component field theory model of the critical behavior is presented. Results for a lattice model originally proposed by Kikuchi are extended with a high temperature series expansion and Monte Carlo simulation. 30 references.
Date: May 1984
Creator: Elser, V.
Partner: UNT Libraries Government Documents Department

Theoretical particle physics

Description: This report discusses the following topics: heavy quark physics; Chiral Perturbation theory; Skyrmions; quarkonia and nuclear matter; parity violating nuclear matrix elements; how precisely can one determine M{sub U}/M{sub D}; weak scale baryogenesis; constraints of baryogenesis form neutrino masses; majorons, double beta decay, supernova 1987A; rare decays; chiral lattice fermions; Pauli-Villars regulator and the Higgs mass bound; and Higgs and Yukawa interactions.
Date: September 30, 1992
Partner: UNT Libraries Government Documents Department

Vacuum Structure of Pure Gauge Theories on the Lattice

Description: Results from simulations on two aspects of quark confinement in the pure gauge sector are presented. First is the calculation of the profile of the flux tube connecting a static q[bar q] pair in SU(2). By use of the Michael sum rules as a constraint, evidence is set forth that the energy density at the center of the flux tube goes to a constant as a function of quark- separation. Slow variation of the width and energy density is not ruled out. Secondly in the confined phase of lattice U(l), the curl of the magnetic monopole current is calculated, and it is shown that the dual London equation is satisfied and that the electric fluxoid is quantized.
Date: January 1, 1992
Creator: Haymaker, Richard W.; Singh, Vandana; Browne, Dana & Wosiek, Jacek
Partner: UNT Libraries Government Documents Department

Theoretical particle physics

Description: We have carried out research in lattice gauge theory, superstring theory, supersymmetry, the solar neutrino puzzle, QCD perturbation theory, and phenomenological models of hadrons. In this report, we summarize our work in each of these areas.
Date: April 1, 1992
Creator: Gottlieb, S.A.; Hendry, A.W.; Kostelecky, V.A. & Lichtenberg, D.B.
Partner: UNT Libraries Government Documents Department