A scalar-pseudoscalar four-Fermi quantum field model in four dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons, the path-integral representation for the generating functional for Green's functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classcal ground-state solution for collective bosons, a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectories for bosons are approximately linear in J, as the experimental trajectories. The existence of fermion bound or excited states depend on the value of the dynamical parameters of the model. For some values of dynamical parameters there are bound states for J = 1 2 and 3 2 . However, for most of other values bound or excited fermion states do not exist.