The Quantum Aspects of Relativistic Fermion Systems with Particle Condensation

A consistent local approach to the study of interacting relativistic fermion systems with a condensation of bare particles in its ground or vacuum state, which may has a finite matter density, is developed. The attention is payed to some of the not so well explored quantum aspects that survive the thermodynamic limit. A 4-vector local field, called the primary statistical gauge field, and a statistical blocking parameter are introduced for a consistent treatment of the problem. The effects of random fluctuations of the fields on local observables are discussed. It is found that quasiparticle contributions are not sufficient to saturate local observables. The property of the primary statistical gauge field are discussed in some detail. Two models for the strong interaction are then introduced and studied using the general framework developed. Four possible phases for these models are found. The possibility of spontaneous CP violation and local fermion creation in two of the four phases is revealed. The implications of the finding on our understanding of some of the strong interaction processes are discussed.