Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory
The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets all gauge (i.e. Gribov) copies originate mainly from the zero-momentum modes of the gauge fields. The removal of the zero–momentum modes turns out to be necessary for reaching the absolute maximum of the gauge functional F(θ) . A new gauge fixing procedure – zero-momentum Lorentz gauge – is proposed.
Chiral Symmetry Restoration in Anisotropic QED(3)
We present results from a Monte Carlo simulation of noncompact lattice QED in three dimensions in which an explicit anisotropy $\ensuremath{\kappa}$ between $x$ and $y$ hopping terms has been introduced into the action. Using a parameter set corresponding to broken chiral symmetry in the isotropic limit $\ensuremath{\kappa}=1$, we study the chiral condensate on ${16}^{3}$, ${20}^{3}$, and ${24}^{3}$ lattices as $\ensuremath{\kappa}$ is varied, and fit the data to an equation of state which incorporates anisotropic volume corrections. The value ${\ensuremath{\kappa}}_{c}$ at which chiral symmetry is apparently restored is strongly volume dependent, suggesting that the transition may be a crossover rather than a true phase transition. In addition we present results on ${16}^{3}$ lattices for the scalar meson propagator, and for the Landau gauge-fixed fermion propagator. The scalar mass approaches the pion mass at large $\ensuremath{\kappa}$, consistent with chiral symmetry restoration, but the fermion remains massive at all values of $\ensuremath{\kappa}$ studied, suggesting that strong infrared fluctuations persist into the chirally symmetric regime. Implications for models of high-${T}_{c}$ superconductivity based on anisotropic ${\mathrm{QED}}_{3}$ are discussed.
Finite-lattice-spacing corrections to masses and g factors on a lattice.
We suggest an alternative method for extracting masses and g factors from lattice calculations. Our method takes account of more of the infrared and ultraviolet lattice effects. It leads to more reasonable results in simulations of QED on a lattice.