PARTICLE MECHANICS MODELS WITH W-SYMMETRIES

We introduce a particle mechanics model with Sp(2M) gauge invariance. Different partial gauge-fixings by means of sl(2) embeddings on the ga uge algebra lead to reduced models which are invariant under diffeomor phisms and classical non-linear W-transformations as the residual gaug e symmetries thus providing a set of models of gauge and matter fields coupled in a W-invariant way. The equations of motion for the matter variables give Lax operators in a matrix form. We examine several exam ples in detail and discuss the issue of integration of infinitesimal W -transformations. (C) 1995 Academic Press, Inc.