Extended gauge invariance in geometrical particle models and the geometry of W-symmetry Original Research Article

We prove that particle models whose action is given by the integrated nth 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 nth 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.