arXiv subjects
Publications and source records attributed to Gary Herling.
We identify the artifact that causes confinement at strong coupling in compact U(1) lattice gauge theory and show that most of the string tension in compact SU(2) lattice gauge theory is due to plaquettes of negative trace.
We have applied a new noncompact, gauge-invariant, Monte Carlo method to simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices. For U(1) the Creutz ratios of the Wilson loops agree with the exact results for beta > 0.5 after a renormalization of the charge. The SU(2) and SU(3) Creutz ratios robustly display quark confinement at beta = 0.5 and beta = 2, respectively. At much weaker coupling, the SU(2) and SU(3) Creutz ratios agree with perturbation theory after a renormalization of the coupling constant. For SU(3) without quarks, our lattice QCD parameter is Lambda_L = 130 +- 18$ MeV.
We explain why compact U(1) confines and how to fix it. We show that plaquettes of negative trace carry most of the confinement signal in compact SU(2). We show how to perform noncompact gauge-invariant simulations without auxiliary fields. We suggest a way to simulate fermions without doublers.
We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate the $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 0.5$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $β= 0.5$ and $β= 2$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant. For $SU(3)$ the scaling window is near $ β= 2 $, and the relation between the string tension $σ$ and our lattice QCD parameter $ Λ_L $ is $\sqrtσ \approx 5 Λ_L$.
We have applied a new gauge-invariant, noncompact, Monte Carlo method to simulate $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$ lattices. The Creutz ratios of the Wilson loops agree with the exact results for $U(1)$ for $β\ge 1$ apart from a renormalization of the charge. The $SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $β= 0.5$ and $β= 1.5$, respectively. At much weaker coupling, the $SU(2)$ and $SU(3)$ Creutz ratios agree with perturbation theory after a renormalization of the coupling constant.