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

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 ${\mathbb{R}}^d$ 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.

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

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• Frenet-Serret dynamics
• Gauge symmetry and W-algebra in higher derivative systems
• Rigid particle revisited: extrinsic curvature yields the Dirac equation
• World sheets of spinning particles
• Hamiltonian Frenet-Serret dynamics
• On the W-geometrical origins of massless field equations and gauge invariance
• Finite BRST Mapping in Higher Derivative Models
• D-dimensional massless particle with extended gauge invariance
• Observers with constant proper acceleration, constant proper jerk, and beyond
• Geometrical model of massive spinning particle in four-dimensional Minkowski space