2-DIMENSIONAL MANY-FERMION SYSTEMS AS VECTOR MODELS

We show that, in two space dimensions, the full many-Fermion interaction has the structure of a vector model at every energy scale. The <<colours>> arise from a decomposition of the Fermi circle into sectors of length set by the energy scale. These sectors play an essential role in summing up the complete perturbation series. The three-dimensional vertex is intermediate between vector and matrix models. In any number of dimensions the reduced interaction is a vector model.