1/N expansion of scalar field theories

Conventional perturbation expansions are limited to investigations of small corrections to classical results, and cannot uncover essentially quantum effects. This criticism does not apply to the 1/N expansion, which includes an infinite number of graphs in each order. This perturbation expansion is applied to scalar field theories with an internal O(N) symmetry, and in particular to four dimensional lambdaphi4 theory and three dimensional phi6 theory which are the most general renormalizable scalar field theories in four and three dimensions, respectively. The problems to be considered are: under what conditions will the O(N) symmetry be spontaneously broken; what is the nature of the ground state; what are the particle propagators