PROGRESS ON PERFECT LATTICE ACTIONS FOR QCD

We describe a number of aspects in our attempt to construct an approxi mately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are the n truncated by imposing 3-periodicity. The spectra of these short rang ed fermions are excellent approximations to continuum spectra. The sam e is true for free gluons. We evaluate the corresponding perfect quark -gluon vertex function, identifying in particular the ''perfect clover term''. First simulations for heavy quarks show that the mass is stro ngly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulat ion for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.