GAUGE-INVARIANT GENERALIZATION OF THE 2D CHIRAL GROSS-NEVEU MODEL

By means of the Lee-Shrock transformation we generalize the 2D Gross-N eveu (GN(2)) model to a U(1) gauge theory with charged fermion and sca lar fields in 2D (chi U-phi 2 model). The chi U-phi 2 model is equival ent to the GN(2) model at infinite gauge coupling. We show that the dy namical fermion mass generation and asymptotic freedom in the effectiv e four-fermion coupling persist also when the gauge coupling decreases . These phenomena are not influenced by the XY(2) model phase transiti on at weak coupling. This suggests that the chi X(phi 2) model is in t he same universality class as the GN(2) model and thus renormalizable.