Discretisation Errors in Landau Gauge on the Lattice

Abstract

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which &Ogr;(a²) errors are removed is presented. &Ogr;(a²) improvement of the gauge fixing condition improves comparison with the continuum Landau gauge in two ways: (1) through the elimination of &Ogr;(a²) errors and (2) through a secondary effect of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition.