Renormalization a la BRS of the non-linear σ-model

We characterize the non-linear O(N+1) σ-model in an arbitrary parametrization with a nihilpotent BRS operator obtained from the symmetry transformation by the use of anticommuting parameters. The identity can be made compatible with the presence of a mass term in the model, so we can analyze its stability and prove that the model is anomaly free. This procedure avoids many problems encountered in the conventional analysis; in particular the introduction of an infinite number of sources coupled to the successive variations of the field is not necessary and the linear O(N) symmetry is respected as a consequence of the identity. The approach may provide useful in discussing the renormalizability of a wider class of models with non-linear symmetries. (orig.)