Related papers: Lattice Landau Gauge and Algebraic Geometry
We address the problem of the gauge fixing versus Gribov copies in lattice gauge theories. For the Landau gauge, results show that a suitable combination of evolutionary algorithms with traditional steepest descent methods identifies the…
We propose a method which allows the generalization of the Landau lattice gauge-fixing procedure to generic covariant gauges. We report preliminary numerical results showing how the procedure works for $SU(2)$ and $SU(3)$. We also report…
We discuss global gauge fixing on the lattice, specifically to the lattice Landau gauge, with the goal of understanding the question of why the process becomes extremely slow for large lattices. We construct an artificial "gauge-fixing"…
An algorithm for gauge fixing to the minimal Landau gauge in lattice QCD is described. The method, a combination of an evolutionary algorithm with a steepest descent method, is able to solve the problem of the nonperturbative gauge fixing.…
We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the…
Gauge-fixing as a sampling procedure of gauge copies provides a possibility to construct well-defined gauges also beyond perturbation theory. The implementation of such sampling strategies in lattice gauge theory is briefly outlined, and…
We address the question of why global gauge fixing, specifically to the lattice Landau gauge, becomes an extremely lengthy process for large lattices. We construct an artificial "gauge-fixing" problem which has the essential features…
We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in…
We present the first numerical implementation of the minimal Landau background gauge for Yang-Mills theory on the lattice. Our approach is a simple generalization of the usual minimal Landau gauge and is formulated for general SU(N) gauge…
In the modern formulation of lattice gauge-fixing, the gauge fixing condition is written in terms of the minima or stationary points (collectively called solutions) of a gauge-fixing functional. Due to the non-linearity of this functional,…
The Laplacian gauge on the lattice is investigated numerically using U(1) and SU(2) gauge fields. The problem of Gribov ambiguities is addressed and to asses the smoothness of the gauge fixed configurations, they are compared to…
We present a new method of gauge fixing to standard lattice Landau gauge, Max Re Tr $\sum_{\mu,x}U_{\mu,x}$, in which the link configuration is recursively smeared; these smeared links are then gauge fixed by standard extremization. The…
We study the problem of critical slowing-down for gauge-fixing algorithms (Landau gauge) in $SU(2)$ lattice gauge theory on $2$ and $4$ dimensional lattices, both numerically and analytically. We consider five such algorithms, and we…
Gribov copies of the vacuum in two dimensional compact U(1) lattice gauge models are constructed. On the basis of this a gauge fixing algorithm is developped, wich finds the minimum of the sum of link field squares. Numerical experience in…
Gauge fixing is a useful tool to simplify calculations. It is also valuable to combine different methods, in particular lattice and continuum methods. However, beyond perturbation theory the Gribov-Singer ambiguity requires further gauge…
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a…
Laplacian gauge fixing was introduced to find a unique representative of the gauge orbit, which on the lattice could be implemented by a ``finite'' algorithm. What was still lacking was a perturbative formulation of this gauge, which will…
We compare two Landau gauge fixing methods, aiming to find the global maximum of the gauge fixing functional. Moreover, a systematic effect of Gribov copies in the gluon and ghost propagators computed in Landau gauge is presented and…
Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In…
Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which ${\cal O}(a^2)$ errors are removed is presented. ${\cal O}(a^2)$ improvement of the gauge fixing condition improves…