  We show an application of the Wilson Renormalization Group (RG) method to a
SU(2 ) gauge field theory in interaction with a massive fermionic doublet. By
choosing suitable boundary conditions to the RG equation, i.e. by requiring the
relevant monomials not present in the classical action to satisfy the
Slavnov-Taylor identities once the cutoffs are removed, we succeed in
implementing the local gauge symmetry. In this way the so called fine-tuning
problem, due to the assignation of boundary conditions in terms of the bare
parameters, is avoided. In this framework, loop expansion is equivalent to the
iterative solution of the RG equation; we perform one loop calculations in
order to determine how much the fermionic matter modifies the asymptotic form
of the couplings. Then we compute the beta-function and we check gluon
transversality. Finally, a proof of perturbative renormalizability is shown.
