Gauge invariant generalization of the 2D chiral Gross-Neveu model
Abstract
By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu (GN2) model to a U(1) gauge theory with charged fermion and scalar fields in 2D ( U φ2 model). The U φ2 model is equivalent to the GN2 model at infinite gauge coupling. We show that the dynamical fermion mass generation and asymptotic freedom in the effective four-fermion coupling persist also when the gauge coupling decreases. These phenomena are not influenced by the XY2 model phase transition at weak coupling. This suggests that the U φ2 model is in the same universality class as the GN2 model and thus renormalizable.
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