Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality. 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 blocking effects, base upon an asymptotic non-thermo ensemble. An application to models are presented to show the importance of the discussions.