arXiv subjects

Ken Yee

Publications and source records attributed to Ken Yee.

14 recordsLinked to original sources

arXiv1995

Demons and Abelian Projection QCD: Action and Crossover

I evaluate S_{APQCD}, the exact action of Abelian projection QCD, using the microcanonical demon method. Starting with a trial action consisting of L=1, L=2, & L=3 LxL plaquettes plus a Smit-van-der-Sijs magnetic monopole ``mass'' operator, I show that coefficients of the L=2 and L=3 plaquettes vanish at all beta_{SU2}. In fact, at strong coupling S_{APQCD} is essentially the 1x1 compact QED action with beta_{U1}=beta_{SU2}/2. Beyond beta_{SU2}>=2, S_{APQCD} gains an exogenous negative 1x1x1 magnetic monopole mass shift. Note that my approach differs fundamentally from the Smit-van-der-Sijs approach in that I do not make an a priori assumption about monopole or plaquette size in S_{APQCD}. Indeed, these results suggest that QCD monopoles are pointlike, in contrast to the ``effective'' condensation picture put forth by Smit and van der Sijs.

hep-lat↗

arXiv1994

Abelian Action for Quark Confinement: A Direct Evaluation

We evaluate S_{APQCD}, the Abelian projection QCD(APQCD) action nonperturbatively on the lattice. For SU(2), we find S_{APQCD} at strong coupling is essentially the compact QED(CQED) action. At weaker coupling, we find S_{APQCD} mutates: it gains additional operators, including an exogenous NEGATIVE magnetic monopole mass shift. As a corollary, since monopoles are condensed in CQED our results prove (vicariously) that SU(2) monopoles are condensed. S_{APQCD} for SU(3) has similar behavior.

hep-ph↗

arXiv1994

Monopoles and Quark Confinement: Introduction and Overview

We (try to) pedagogically explain how monopoles arise in QCD, why maximal Abelian(MA) gauge is ``special'' for monopole study, the Abelian projection in MA gauge, its resultant degrees of freedom(photons, monopoles and charged matter fields), and the QCD-equivalent action in terms of these degrees of freedom. Then we turn to more recent developments in the subject: Abelian dominance, large $N$ behavior of Abelian projected QCD, mass of the charged matter fields, notion of an effective photon-monopole action obtained by integrating out the charged matter fields, and problems encountered in the recent evaluation of this effective action using the microcanonical demon method on the lattice.

hep-ph↗

arXiv1994

Fractal Dimension of Gauge-fixing Defects

The fractal dimension $D_f$ of sites resisting Landau or maximal Abelian(MA) gauge fixing in lattice $SU(3)$ gluodynamics is defined and computed. In Landau gauge such sites clump into $D_f\sim 1$ clusters in the confining phase. In the finite temperature phase their dimensionality drops to $D_f < 1$, that is, clustering seems to dissipate. In contrast, MA gauge resistant sites fail to exhibit a notable tendency to cluster at any temperature.

hep-lat↗

arXiv1994

Temperature Dependence of Extended and Fractional SU(3) Monopole Currents

We examine in pure SU(3) the dependence of extended monopole current k and cross-species extended monopole current k^{cross} on temperature t, monopole size L, and fractional monopole charge 1/q. We find that features of both k and k^{cross} are sensitive to t for a range of L and q. In particular, the spatial-temporal asymmetry ratios of both k and k^{cross} are sensitive over a range of L and q to the SU(3) deconfinement transition. The motivation for studying cross, extended, and fractional monopoles in SU(3) is given.

hep-lat↗

arXiv1993

Compact U(1)xU(1) Model with Minimal Interspecies Interaction

We introduce a minimally interacting pure gauge compact U(1)xU(1) model consistent with abelian projection symmetries. This paradigm, whose interactions are entirely due to compactness, illustrates how compactness can contribute to interspecies interactions. Furthermore, it has a much richer phase structure(including a magnetically confining phase) than obtained by naively tensoring together two compact U(1) copies.

hep-lat↗

arXiv1993

Towards an Abelian Formulation of Lattice QCD Confinement

We probe for operators occurring in the APQCD(``abelian-projected QCD'') action by evaluating abelian-projected $1$-plaquette spectral densities in pure gauge $SU(3)$ fixed to maximal abelian gauge. Couplings $B_{APQCD}(q,L)$ are extracted from the spectral densities for each representation $q$, $L\times L$ plaquette. While APQCD is dominated by a $q=L=1$ resonance, we also find evidence for weakly coupled $L=2$ plaquettes. Moreover, since $B_{APQCD}(1,1) > B_{QED}(1,1)$ even if $β_{QED} > β_c$, $L>1$ plaquettes must be significant since APQCD is confining.

hep-lat↗

arXiv1993

Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics

't~Hooft's abelian projection of $SU(N)$ gauge theory yields $N$ mutually constrained, compact abelian fields which are permutationally equivalent. We formulate the notion of ``species permutation'' symmetry of the $N$ abelian projection fields and discuss its consequences for cross-species correlators. We show that at large $N$ cross-species interactions are ${1\over N}$ suppressed relative to same-species interactions. Numerical simulations at $N=3$ support our symmetry arguments and reveal the existence of inter-species interactions of size ${\cal O\/}\bigl({1\over N-1}\bigr)$ as analytically predicted.

hep-lat↗

arXiv1993

Compact QED in Landau Gauge: a lattice gauge fixing case study

We derive different representations of compact QED fixed to Landau gauge by the lattice Faddeev-Popov procedure. Our analysis finds that (A)Nielsen-Olesen vortices arising from the compactness of the gauge-fixing action are {\it quenched\/}, that is, the Faddeev-Popov determinant cancels them out and they do not influence correlation functions such as the photon propagator; (B)Dirac strings are responsible for the nonzero mass pole of the photon propagator. Since in $D=3+1$ the photon mass undergoes a rapid drop to zero at $β_c$, the deconfinement point, this result predicts that Dirac strings must be sufficiently dilute at $β> β_c$. Indeed, numerical simulations reveal that the string density undergoes a rapid drop to near zero at $β\sim β_c$.

hep-lat↗

arXiv1992

Dirac Strings and the Nonperturbative Photon Propagator in Compact QED

A ``3D'' Mathematica@-generated picture of monopoles and Dirac strings in $D=2+1$ compact QED is given. In the Villain approximation, the monopole part of the partition function factorizes from the Dirac string part, which generates the photon propagator. Numerical experiments in exact compact QED confirm this result: photon mass pole $M_γ$, originally nonzero, is insensitive to monopole prohibition but almost vanishes if Dirac strings are prohibited.

hep-lat↗

arXiv1992

Decoupling of Photon Propagator in Compact QED

In compact QED$_{2+1}$ quantum monopole fluctuations induce confinement by expelling electric flux in a dual Meissner effect. Guided by Landau-Ginzburg theory, one might guess that the inverse London penetration depth $λ^{-1}$---the only physical mass scale---equals the photon propagator mass pole $M_γ$. I show this is not true. Indeed, in the Villain approximation the monopole part of the partition function factorizes from the photon part, whose dynamical variables are Dirac strings. Since Dirac strings are gauge-variant structures, I conclude that $M_γ$ is physically irrelevant: it is not a blood relative of $λ$ or any other quantity in the gauge-invariant sector. This result is confirmed by numerical simulations in the full theory, where $M_γ$ is not sensitive to monopole prohibition but essentially vanishes if Dirac strings are prohibited.

hep-lat↗

arXiv1992

Introduction to Lattice Gaugefixing and Effective Quark and Gluon Masses

This talk was presented to a non-lattice audience at the June, 1992 Paris Workshop on QCD Vacuum Structure. We report on the status of quark and gluon propagators in quenched, gaugefixed lattice QCD. In Landau gauge we find that the effective quark mass in the chiral limit is $M_q \sim 350(40)MeV$. Quark and gluon propagators, the slope of the quark dispersion relation, and effective masses all appear to depend on gauge. A link-chain picture of lattice gaugefixing in the color $N\to\infty$ and strong coupling limit, where the system becomes almost solvable, supports the gauge variance of these numerical results. Subscribers will be given one Postscript file, the Figure included. Latex and Axis versions available from KY at kyee@rouge.phys.lsu.edu on request.

hep-lat↗

arXiv1992

Gauge Dependence of Effective Quark Mass and Matrix Elements in Gaugefixed Large $N$ Strong Coupling Lattice QCD

In conjunction with recent numerical \hbox{$λ~\partial_0 A_0 + \nabla\cdot\vec{A} =0$} ``$λ$-gauge'' results reported in a companion paper, we construct an $N\to\infty$ Wilson loop picture of $λ$-gaugefixing in which (I)the $λ$-gauge expectation value of a link chain $C$ is the weighted sum over Wilson loops made by joining to $C$ all selfavoiding chains $\widetilde{C}$ closing $C$. (II)Weights $A_{\widetilde{C}}$, containing all the $λ$-dependence, are given by the $β=0$ $λ$-gauge expectation value of $\widetilde{C}$. (III)$A_{\widetilde{C}}$ equals path-products of coefficients from the trace expansion of the gaugefixing Boltzmann weight. From (II) and (III) we deduce formulas for $β=0$ quark matrix elements. We find that $M_q^{(λ)}$ decreases with increasing $λ$; the quark propagator dispersion relation is not covariant when $λ\ne 1$; and $ΔI=1/2$ matching coefficients are $λ$-independent. These strong coupling features are qualitatively consistent with numerical $β=5.7$ and $6.0$ results briefly described here for comparison purposes but mainly presented in a companion paper.

hep-lat↗

arXiv1992

Central Charge of the Parallelogram Lattice Strong Coupling Schwinger Model

We put forth a Fierzed hopping expansion for strong coupling Wilson fermions. As an application, we show that the strong coupling Schwinger model on parallelogram lattices with nonbacktracking Wilson fermions span, as a function of the lattice skewness angle, the $Δ= -1$ critical line of $6$-vertex models. This Fierzed formulation also applies to backtracking Wilson fermions, which as we describe apparently correspond to richer systems. However, we have not been able to identify them with exactly solved models.

hep-lat↗