1/N

The solution to families of field theories with symmetry group SO(N) that become larger as N becomes larger possesses an expansion in powers of 1/N. This expansion is the subject of this paper. The 1/N expansion is developed for theory and applied to two two-dimensional models with similar combinatoric structures, the Gross-Neveu model and the CP N-1 model. Asymptotic freedom, dynamical symmetry breaking, and dimensional transmutation are exhibited in the models. It is also possible that 1/N expansion might be applied to quantum chromodynamics, and conjectural work is carried out in this area. 1/N expansion is much more difficult in SU(N) because fields transform according to the adjoint (not vector) representation. Abstract arguments are made concrete by the example of the 't Hooft model, large-N chromodynamics in two space-time dimensions. Witten's theory, and the special problem of baryons, are considered. In conclusion, the lineaments of the mesons emerge clearly and unambigously from chromodynamics by the 1/N method. But Witten's theory, though an analytic triumph, is found to be a phenomenological disaster