D-dimensional massless particle with extended gauge invariance

Abstract

We propose the model of $D-$dimensional massless particle whose Lagrangian is given by the $N-$th extrinsic curvature of world-line. The system has $N+1$ gauge degrees of freedom constituting $W-$like algebra; the classical trajectories of the model are space-like curves which obey the conditions $k_{N+a}=k_{N-a}$, $k_{2N}=0$, $a=1,...,N-1$, $N\le [(D-2)/2]$, while the first $N$ curvatures $k_i$ remain arbitrary. We show that the model admits consistent formulation on the anti-De Sitter space. The solutions of the system are the massless irreducible representations of Poincaré group with $N$ nonzero helicities, which are equal to each other.

5pages, Talk given at IX Colloquium on Quantum groups and Integrable models (June 22-24, 2000, Prague)

References in corpus (4)

• Classical A_n--W-Geometry
• W-symmetry and the rigid particle
• Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature
• Extended Gauge Invariance in Geometrical Particle Models and the Geometry of W-Symmetry