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arXiv · hep-th/9504071

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

E. Ramos·J. Roca
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Abstract

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 $\reals^d$ in terms of a standard relativistic particle in $S^{d-n}$. We ``prove by example'' that the algebra of these infinitesimal gauge invariances is nothing but $\W_{n+2}$, 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.

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E. Ramos, J. Roca. 1996-02-22. Extended Gauge Invariance in Geometrical Particle Models and the Geometry of W-Symmetry. https://doi.org/10.1016/0550-3213(95)00329-q

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