SYSTEMATIC 1 N CORRECTIONS FOR BOSONIC AND FERMIONIC VECTOR MODELS WITHOUT AUXILIARY FIELDS/

In this paper, colorless bilocal fields are employed to study the larg e N limit of both fermionic and bosonic vector models. The Jacobian as sociated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective act ion. This effective action is shown to reproduce the familiar perturba tive expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action accounts co rrectly for the Fermi statistics. The theory also is studied nonpertur batively. The stationary points of the effective action are shown to p rovide the usual large N gap equations. The homogeneous equation assoc iated with the quadratic (in the bilocals) action is simply the two pa rticle Bethe-Salpeter equation. Finally, the leading correction in 1/N is shown to be in agreement with the exact S matrix of the model.