  We present a new method solving Schwinger-Dyson equations in gauge theories
via imaginary part analysis. The self-consistency equation for the fermion
self-energy can be reduced from a numerical unstable eigenvalue problem to a
finite dimensional integral which can be solved easily. We can therefore derive
relations between the dynamically generated fermion mass, the coupling, the
gauge boson mass and the cutoff. For infinite cutoff the fermion mass is
independent of the gauge boson mass which should be the relevant scale. Thus
for a defined fermion mass it is necessary to incorporate a running coupling
constant. Within 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.
