  Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson
relation, is perhaps the best known formulation of QCD with a finite cutoff. It
reproduces all the low energy QCD phenomenology associated with chiral symmetry
at finite lattice spacings. In particular it explains the origin of massless
pions due to spontaneous chiral symmetry breaking and leads to new ways to
approach the U(1) problem on the lattice. Here we show these results in the
path integral formulation and derive for the first time in lattice QCD a known
formal continuum relation between the chiral condensate and the topological
susceptibility. This relation leads to predictions for the critical behavior of
the topological susceptibility near the phase transition and can now be checked
in Monte-Carlo simulations even at finite lattice spacings.
