The W₃ particle

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.