  We discuss a proposal for the construction of lattice QCD with gauge action,
fermionic action, theta-term, and the operators all based on the lattice Dirac
operator D with exact chiral symmetry. The simplest regularization of this type
uses the proposition that the classical limit of scalar gauge density
associated with trace of D is (up to an additive constant) proportional to
tr(FF), while the corresponding operator is local. More general formulations
from this class are considered with the aim of exposing interrelations between
gauge and fermionic aspects of QCD which are otherwise hidden in generic
formulations. Possible utility of these formulations for exploring QCD vacuum
structure is emphasized.
