Extended Gauge Invariance in Geometrical Particle Models and the Geometry of W - Symmetry

We prove that particle models whose action is given by the integrated n-th curvature function over the world line possess n+ 1 gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by rephrasing the n-th curvature model in Rd in terms of a standard relativistic particle in Sd−n. We “prove by example” that the algebra of these infinitesimal gauge invariances is nothing but Wn+2, thus providing a geometrical picture of the W-symmetry for these models. As a spin-off of our approach we give a new global invariant for four-dimensional curves subject to a curvature constraint. † e-mail: [email protected] ‡ e-mail: [email protected]