  We consider hamiltonian models representing an arbitrary number of spin $1/2$
fermion quantum fields interacting through arbitrary processes of creation or
annihilation of particles. The fields may be massive or massless. The
interaction form factors are supposed to satisfy some regularity conditions in
both position and momentum space. Without any restriction on the strength of
the interaction, we prove that the Hamiltonian identifies to a self-adjoint
operator on a tensor product of anti-symmetric Fock spaces and we establish the
existence of a ground state. Our results rely on new interpolated $N_\tau$
estimates. They apply to models arising from the Fermi theory of weak
interactions, with ultraviolet and spatial cut-offs.
