Dynamical generation of fermion mass

The problem of dynamical generation of fermion masses and chiral symmetry breaking is studied. Another formation for the Chang-Chang approach, which is based on the Nambu-Jona-Lasino (NJL) mechanism, is presented. It is shown that the solution m = e/sup 1/6/ is independent of the two-loop constant. The gauge independence of the solution of the self-consistency condition in two loop accuracy is shown through an explicit calculation in arbitrary gauge and renormalization group analysis. The up-down quark mass difference is calculated by including QED interaction as perturbation to the QCD calculation and in two-loop accuracy the result is of the right sign and also of right order of magnitude. The supersymmetric extension of NJL model (SNJL) is studied. It is shown that there is a nontrivial solution of self consistency condition for the SNJL model. Using the bifurcation theory, the conditions of the stable nontrivial solution of the NJL and SNJL models are found and the critical temperature is calculated. It is shown that in supersymmetric gauge field theories chiral symmetry is broken via NJL mechanism and the dynamically generated mass is M /sub c(susy)/e/sup 1/2/