A mean field theory of study of lattice gauge theory with finite temperature and with finite fermion density

We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data. (orig.)