A Framework for Systematic Study of QCD Vacuum Structure II: Coherent Lattice QCD

We propose the formulation of lattice QCD wherein all elements of the theory (gauge action, fermionic action, θ–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 gauge density associated with trace of D is (up to an additive constant) proportional to trF 2, 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.