Lattice topological charges and the H-gauge

One major problem still to be solved in pure gauge lattice gauge theory is the development of an updating scheme that beats critical slowing down. Long range correlations have been observed in extensive quantities like blocked Wilson loops or topological charge, for configurations generated with local updating schemes like Metropolis updating and pseudo-heatbath. Over-relaxed algorithms improve the situation but are not able to bring the dynamical critical exponent z below 1. Algorithms have been developed for spin and other non-gauge systems but the generalisation to gauge systems has not been achieved apart from the Z2 model. That line may possibly generalise to U(1), but the generalisation to SU(N) is unlikely. We try a different method, that makes changes at physical scales to configurations. The results will be described elsewhere. In this paper we discuss two of the technical issues. One is the construction of lattice topological charges, the other the definition of a suitable gauge. (author)