  It is found that, in addition to the conventional ones, a local approach to
the relativistic quantum field theories at both zero and finite density
consistent with the violation of Bell like inequalities should contain, and
provide solutions to at least three additional problems, namely, 1) the
statistical gauge invariance 2) the dark components of the local observables
and 3) the fermion statistical block effects, base upon an asymptotic
non-thermo ensemble. An application to models are presented to show the
relevance of the discussions.
