FERMION MASS GENERATION IN THE D-DIMENSIONAL THIRRING MODEL AS A GAUGE-THEORY

Based on the Schwinger-Dyson (SD) equation, the fermion mass generatio n is studied further in the D(2 < D < 4)-dimensional Thirring model as a gauge theory previously proposed. Using a certain approximation on the kernel, we analytically obtain explicit form of the dynamical mass of the fermion and the critical line in (N, 1/g) space, where N is th e number of fermions and g is the dimensionless vector-type four-fermi on coupling constant. This analytical result is confirmed by the numer ical solution for the SD equation with the exact form of the kernel in (2+1) dimensions.