  In the paper, within the background field method, the renormalization and the
gauge dependence is studied as for an SU(2) Yang-Mills theory with multiplets
of spinor and scalar fields. By extending the quantum action of the
BV-formalism with an extra fermion vector field and a constant fermion
parameter, the multiplicative character of the renormalizability is proven. The
renormalization of all the physical parameters of the theory under
consideration is shown to be gauge-independent.
