IMAGINARY PART ANALYSIS IN DYNAMICAL SYMMETRY-BREAKING

We present a new method for solving Schwinger-Dyson equations in gauge theories via an imaginary part analysis. The self-consistency equatio n for the fermion self-energy can be reduced from a numerical unstable eigenvalue problem to a finite-dimensional integral which can be solv ed easily. We can therefore derive relations between the dynamically g enerated fermion mass, the coupling, the gauge boson mass and the cuto ff. For infinite cutoff the fermion mass is independent of the gauge b oson mass which should be the relevant scale, Thus for a defined fermi on mass it is necessary to incorporate a running coupling constant. Wi thin our framework this is possible in a well-defined way, The results are reasonable and in agreement with the renormalization group in the asymptotic regime. (C) 1998 Elsevier Science B.V.