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

Original · EN

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 ᵈ 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 ₙ₊₂, thus providing a geometrical picture of the -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.