Abstract:
We describe a number of aspects in our attempt to construct
an approximately perfect lattice action for QCD. Free quarks
are made optimally local on the whole renormalized
trajectory and their couplings are then truncated by
imposing 3-periodicity. The spectra of these short ranged
fermions are excellent approximations to continuum spectra.
The same 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 strongly
renormalized, but again the renormalized theory agrees very
well with continuum physics. Furthermore we describe the
multigrid formulation for the non-perturbative perfect
action and we present the concept of an exactly (quantum)
perfect topological charge on the lattice.
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