An Intrinsic 1/ N Expansion for Many-Fermion Systems

The 1/ N expansion is a popular tool for investigating non-perturbative long-range phenomena. In many-body models, discretization of the Fermi surface naturally introduces a many-component picture. If, for example, number symmetry is broken, N ≈ (exp [1/λ]) ( d -1) , where λ > 0 is the bare coupling constant. We expect that this intrinsic 1/ N expansion appears whenever the “free propagator” of the system is singular along a hypersurface (for instance, in the Anderson model for localized and extended states).