Minimal U(1) Gauge Fields in Two Dimensions

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 a two dimensional Higgs model with fixed length scalar field is reported and the extension to three and four dimensional U(1) and four dimensional SU(2) gauge theories is briefly discussed.