  The motivation for the development of a local finite density theory is
discussed. One of the problems related to an instability in the baryon number
fluctuation of the chiral symmetry breaking phase of the quark system in the
local theory is shown to exist. Such an instability problem is removed by
taking into account the statistical blocking effects for the quark propagator,
which depends on a macroscopic {\em statistical blocking parameter} $\epsilon$.
This new frame work is then applied to study color superconducting phase of the
light quark system.
