  We perform the numerical simulation of the two dimensional chiral Gross Neveu
model using the Kogut-Susskind(KS) fermion. In the case of SU(4), the
Kosterlitz-Thouless phase transition happens at some critical value of the
coupling constant. In the case of one flavour, there exists the strong coupling
phase in which the correlation functions vanish and the general covariance is
realized in the quantum field thoery through the dynamical process.
