  In the present work we have developed a large-N expansion for the $t-J$ model
based on the path integral formulation for Hubbard-operators. Our large-N
expansion formulation contains diagrammatic rules, in which the propagators and
vertex are written in term of Hubbard operators. Using our large-N formulation
we have calculated, for J=0, the renormalized $O(1/N)$ boson propagator. We
also have calculated the spin-spin and charge-charge correlation functions to
leading order 1/N. We have compared our diagram technique and results with the
existing ones in the literature.
