A NOVEL LOOK AT THE MICHAEL LATTICE SUM RULES

We reconsider the derivation of the Michael lattice sum rules, which relate the energy and action stored in a flux tube of a quark-antiquark pair to the static interquark potential, and show that they require essential corrections. We then find, using the coupling constant sum rule of Karsch, that the total Minkowski field energy does not match the interquark potential, if one follows conventional notions. The implications of this result are discussed.Comment: 8 pages, Plain Te

Dual Abrikosov Vortices in Confining Theories

The spacial distribution of fields and currents in confining theories can give direct evidence of dual superconductivity. We would like to discuss the techniques for finding these properties and calculating the superconductivity parameters in lattice simulations. We have seen dual Abrikosov vortices directly in pure U(1) and SU(2) and others have also seen them in SU(3). In the non-Abelian cases the system appears to be near the borderline between type I and II. We also discuss the response of the supercurrents to external fields.Comment: 8 pages, Latex , 5 ps figure files attached (figs. 1,3,4,5,6) Talk, Proceedings at CONFINEMENT95, Osaka, March 199

Confinement studies in lattice QCD

We describe the current search for confinement mechanisms in lattice QCD. We report on a recent derivation of a lattice Ehrenfest-Maxwell relation for the Abelian projection of SU(2) lattice gauge theory. This gives a precise lattice definition of field strength and electric current due to static sources, charged dynamical fields, gauge fixing and ghosts. In the maximal Abelian gauge the electric charge is anti-screened analogously to the non-Abelian charge.Comment: Talk given at the Symposium in Honor of Dick Slansky, Los Alamos, May 20-21 1998, to be published in Phys. Rep., Latex 2e uses class file elsart.cl

Consistent Definitions of Flux and Electric and Magnetic Current in Abelian Projected SU(2) Lattice Gauge Theory

Through the use of a lattice U(1) Ward-Takahashi identity, one can find a precise definition of flux and electric four-current that does not rely on the continuum limit. The magnetic four-current defined for example by the DeGrand-Toussaint construction introduces order a^2 errors in the field distributions. We advocate using a single definition of flux in order to be consistent with both the electric and magnetic Maxwell's equations at any lattice spacing. In a U(1) theory the monopoles are slightly smeared by this choice, i.e. are no longer associated with a single lattice cube. In Abelian projected SU(2) the consistent definition suggests further modifications. For simulations in the scaling window, we do not foresee large changes in the standard analysis of the dual Abrikosov vortex in the maximal Abelian gauge because the order a^2 corrections have small fluctuations and tend to cancel out. However in other gauges, the consequences of our definitions could lead to large effects which may help in understanding the choice of gauge. We also examine the effect of truncating all monopoles except for the dominant cluster on the profile of the dual Abrikosov vortex.Comment: 12 pages, 4 eps figures, Confinement 2003 contributed tal

On the Effective Potential for Local Composite Operators

We show that the effective potential for local composite operators is a useful object in studing dynamical symmetry breaking by calculating the effective potential for the local composite operators $\bar{\psi} \psi$ and $\phi^2$ in the Gross-Neveu (GN) and O(N) models, respectively. Since the effective potential for local composite operators can be calculated by using the Cornwall-Jackiw-Tomboulis (CJT) effective potential in theory with additional bare mass terms, we show that divergences in the effective potential for local composite operators are the same as in the CJT effective potential. We compare the results obtained with the results give by the auxiliary field method.Comment: 17 pages, LaTeX, the analysis of the O(N) model with finite cut-off have been reconsidered and the corresponding important reference have been adde