Confinement and Topological Charge in the Abelian Gauge of QCD

We study the relation between instantons and monopoles in the abelian gauge. First, we investigate the monopole in the multi-instanton solution in the continuum Yang-Mills theory using the Polyakov gauge. At a large instanton density, the monopole trajectory becomes highly complicated, which can be regarded as a signal of monopole condensation. Second, we study instantons and monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA) gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find monopole dominance for instantons in the confinement phase even at finite temperatures. A linear-type correlation is found between the total monopole-loop length and the integral of the absolute value of the topological density (the total number of instantons and anti-instantons) in the MA gauge. We conjecture that instantons enhance the monopole-loop length and promote monopole condensation.Comment: 3 pages, LaTeX, Talk presented at LATTICE96(topology

Stretching in a model of a turbulent flow

Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds number and the maximum Lyapunov exponent, which is similar to that for a turbulent flow with the same energy spectrum. Our results show that the Lyapunov exponents are sensitive to the advection of small eddies by large eddies, which can be explained by considering the Lagrangian correlation time of the smallest scales. We also relate the number of stagnation points within a flow to the maximum Lyapunov exponent, and suggest a linear dependence between the two characteristics.Comment: 7 pages, 10 figure

Weyl Invariant Formulation of Flux-Tube Solution in the Dual Ginzburg-Landau Theory

The flux-tube solution in the dual Ginzburg-Landau (DGL) theory in the Bogomol'nyi limit is studied by using the manifestly Weyl invariant form of the DGL Lagrangian. The dual gauge symmetry is extended to $[U(1)]_m^3$, and accordingly, there appear three different types of the flux-tube. The string tension for each flux-tube is calculated analytically and is found to be the same owing to the Weyl symmetry. It is suggested that the flux-tube can be treated in quite a similar way with the Abrikosov-Nielsen-Olesen vortex in the U(1) Abelian Higgs theory except for various types of flux-tube.Comment: 12 pages, revtex, no figur

Monopole Clustering and Color Confinement in the Multi-Instanton System

We study color confinement properties of the multi-instanton system, which seems to carry an essence of the nonperturbative QCD vacuum. Here we assume that the multi-instanton system is characterized by the infrared suppression of instantons as $f(\rho)\sim \rho^{-5}$ for large size $\rho$. We first investigate a monopole-clustering appearing in the maximally abelian (MA) gauge by considering the correspondence between instantons and monopoles. In order to clarify the infrared monopole properties, we make the ``block-spin'' transformation for monopole currents. The feature of monopole trajectories changes drastically with the instanton density. At a high instanton density, there appears one very long and highly complicated monopole loop covering the entire physical vacuum. Such a global network of long-monopole loops resembles the lattice QCD result in the MA gauge. Second, we observe that the SU(2) Wilson loop obeys an area law and the static quark potential is approximately proportional to the distance $R$ between quark and anti-quark in the multi-instanton system using the SU(2) lattice with a total volume of $V=(10 fm)^4$ and a lattice spacing of $a=0.05 fm$. We extract the string tension from the $5 \times 10^{6}$ measurements of Wilson loops. With an instanton density of $(N/V)=(1/fm)^4$ and a average instanton size of $\bar{\rho}=0.4 fm$, the multi-instanton system provides the string tension of about $0.4 GeV/fm$

Flux-Tube Ring and Glueball Properties in the Dual Ginzburg-Landau Theory

An intuitive approach to the glueball using the flux-tube ring solution in the dual Ginzburg-Landau theory is presented. The description of the flux-tube ring as the relativistic closed string with the effective string tension enables us to write the hamiltonian of the flux-tube ring using the Nambu-Goto action. Analyzing the Schr\"odinger equation, we discuss the mass spectrum and the wave function of the glueball. The lowest glueball state is found to have the mass $M_G \sim 1.6 GeV$ and the size $R_G \sim 0.5 fm$.Comment: 24 pages, 6 figures, revte

Sarcopenia; Aging-related loss of muscle mass and function

Sarcopenia is a loss of muscle mass and function in the elderly that reduces mobility, diminishes quality of life, and can lead to fall-related injuries, which require costly hospitalization and extended rehabilitation. This review focuses on the aging-related structural changes and mechanisms at cellular and subcellular levels underlying changes in the individual motor unit: specifically, the perikaryon of -motoneuron, its neuromuscular junction(s), and the muscle fibers that it innervates. Loss of muscle mass with aging, which is largely due to the progressive loss of motoneurons, is associated with reduced muscle fiber number and size. Muscle function progressively declines because motoneuron loss is not adequately compensated by reinnervation of muscle fibers by the remaining motoneurons. At the intracellular level, key factors are qualitative changes in posttranslational modifications of muscle proteins and the loss of coordinated control between contractile, mitochondrial, and sarcoplasmic reticulum protein expression. Quantitative and qualitative changes in skeletal muscle during the process of aging also have been implicated in the pathogenesis of acquired and hereditary neuromuscular disorders. In experimental models, specific intervention strategies have shown encouraging results on limiting deterioration of motor unit structure and function under conditions of impaired innervation. Translated to the clinic, if these or similar interventions, by saving muscle and improving mobility, could help alleviate sarcopenia in the elderly, there would be both great humanitarian benefits and large cost savings for health care systems