$1/N$ expansion for scalar fields

Models of scalar field theories with a large number $N$ of isotopic degrees of freedom are considered. A theory of perturbations with respect to a small parameter is developed in the formalism of path integration for a space-time dimension $D=2,3,4$.The particle spectrum obtained in basic order with respect to $N^{-1}$ is compared with the spectrum in the path approach. It is shown that when $D=4$ the chiral field model is turned, as a result of renormalization, into a model with four interactions. The limitations of the applicability of the $1/N$ expansion are discussed.