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

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

1995-04-13

arxiv.org/abs/hep-th/9504071v2

Nucl.Phys. B452 (1995) 705-723

Physics

High Energy Physics

High Energy Physics - Theory

plain TeX (macros included). Slightly modified version published in Nuc. Phys. B

Scientific paper

10.1016/0550-3213(95)00329-Q

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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