Dynamical Symmetry Breaking in a Gauge Theory “ Thirring Model ” ∗

Dynamical fermion mass generation is studied in the three-dimensional Thirring model reformulated as a gauge theory by introducing hidden local symmetry. The analysis by use of Schwinger-Dyson equation is shown to exhibit a critical behavior as the number N of four-component fermions approaches Ncr = 128/3π 2. When we consider the models of massless self-interacting fermions, a central issue is the dynamical fermion mass generation. If it is indeed the case, intriguing detailed questions are whether the model of interest is shown to exhibit a critical behavior as the number N of fermions approaches Ncr and, in three dimensions, whether the pattern of dynamically generated masses preserves the parity or not. In this report we address ourselves to the problem of dynamical symmetry breaking in the Thirring model of N massless four-component fermions. (For the notations and the detailed calculations, see Ref.[1].)