Critical O(N) - vector nonlinear sigma - models: A resume of their field structure

The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d=2 and d=4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so.