The W_3 particle

TL;DR

This paper demonstrates that the W_3 algebra describes the symmetries of a rigid-particle model based on extrinsic curvature, linking it to the Boussinesq operator and exploring connections with the KdV operator.

Contribution

It establishes the W_3 algebra as the symmetry algebra of a rigid-particle and relates the equations of motion to the Boussinesq operator, providing new insights into particle symmetries.

Findings

W_3 algebra is the symmetry of the rigid-particle

Equations of motion relate to the Boussinesq operator

Connection between zero-curvature gauge and relativistic particle

Abstract

We show that W_3 is the algebra of symmetries of the ``rigid-particle'', whose action is given by the integrated extrinsic curvature of its world line. This is easily achived by showing that its equation of motion can be written in terms of the Boussinesq operator. We also show how to obtain the equations of motion of the standard relativistic particle provided it is consistent to impose the ``zero-curvature gauge'', and comment about its connection with the KdV operator.