Thirring model in lower dimensions: Nonperturbative approaches

A reformulation of the Thirring model as a gauge theory on both continuum spacetime and discretized lattice is reviewed. In (1+1) dimensions, our result reproduces consistently the bosonization of the massless Thirring model. In (2+1) dimensions, the analysis by use of Schwinger-Dyson equation is shown to exhibit dynamical fermion mass generation when the number $N$ of four-component fermions is less than the critical value $N_{cr}= 128/3\\pi^{2}$.