Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite densityproblems based on the principle of locality. It is shown that, inaddition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems,namely, i) the statistical gauge invariance; ii) the dark components ofthe local observables; and iii) the fermion statistical blocking effects,based upon an asymptotic nonthermal ensemble. An application to modelsis presented to show the importance of the discussions.