Hodge gauge fixing in three dimensions

A progress report on experiences with a gauge fixing method proposed in LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized at each site, followed by gauge fixing the diagonal (Cartan) part of the links to Coulomb gauge using the residual abelian freedom. The Cartan sector of the link field is separated into the physical gauge field $\alpha^{(f)}_\mu$ responsible for producing $f^{\rm Cartan}_{\mu\nu}$, the pure gauge part, lattice artifacts, and zero modes. The gauge transformation to the physical gauge field $\alpha^{(f)}_\mu$ is then constructed and performed. Compactness of the lattice fields entails issues related to monopoles and zero modes which are addressed.