  In the framework of an approach to bosonization based on the use of fermionic
composites as fundamental variables, a quadratic action in even Grassmann
variables with the quantum numbers of the pions has been constructed. It
includes the sigma-field in order to be invariant under SU(2)_L times SU(2)]_R
transformations over the quarks. This action exhibits the Goldstone phenomenon
reducing its symmetry to the O(3) isospin invariance. A squared mass for the
pions is generated according to PCAC. The model has been investigated in the
Stratonovitch-Hubbard representation, in which form it is reminiscent of the
Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in
inverse powers of the index of nilpotency of the mesonic fields (which is 24),
is generated. The way it might be used in a new perturbative approach to QCD is
outlined.
