STOCHASTIC QUANTIZATION OF NAMBU-JONA-LASINIO MODEL

Stochastic quantizations of the Nambu-Jona-Lasinio model with and without the bare mass term are carried out. It is shown that, although the linear fermion Langevin equation is not chiral-invariant, one obtains the chiral-invariant effective potential in the equilibrium limit when the bare mass vanishes. Numerical solutions of the growing order parameter and two kinds of effective potentials, which take qualitatively different forms if the bare mass is nonvanishing, are presented.