  We propose the formulation of lattice QCD wherein all elements of the theory
(gauge action, fermionic action, theta-term, and all operators) are constructed
from a single object, namely the lattice Dirac operator D with exact chiral
symmetry. Several regularizations of this type are suggested via constructing
scalar densities (gauge actions) that are explicit functions of D. The simplest
of these is based on the proposition that classical limit of density associated
with Tr D is (up to an additive constant) proportional to FF, while the
corresponding operator is local. The possibilities of explicit interrelations
between gauge and fermionic aspects of the theory are emphasized together with
the utility of such formulations for exploring the QCD vacuum structure.
