Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory

Abstract

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

21 pages, 2 Postscript figures, LaTeX

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