  We show how to obtain all covariant field equations for massless particles of
arbitrary integer, or half-integer, helicity in four dimensions from the
quantization of the rigid particle, whose action is given by the integrated
extrinsic curvature of its worldline, {\ie} $S=\alpha\int ds \kappa$. This
geometrical particle system possesses one extra gauge invariance besides
reparametrizations, and the full gauge algebra has been previously identified
as classical $\W_3$. The key observation is that the covariantly reduced phase
space of this model can be naturally identified with the spinor and twistor
descriptions of the covariant phase spaces associated with massless particles
of helicity $s=\alpha$. Then, standard quantization techniques require $\alpha$
to be quantized and show how the associated Hilbert spaces are solution spaces
of the standard relativistic massless wave equations with $s=\alpha$.
Therefore, providing us with a simple particle model for Weyl fermions
($\alpha=1/2$), Maxwell fields ($\alpha=1$), and higher spin fields. Moreover,
one can go a little further and in the Maxwell case show that, after a suitable
redefinition of constraints, the standard Dirac quantization procedure for
first-class constraints leads to a wave-function which can be identified with
the gauge potential $A_\mu$. Gauge symmetry appears in the formalism as a
consequence of the invariance under $\W_3$-morphisms, that is, exclusively in
terms of the extrinsic geometry of paths in Minkowski space. When all gauge
freedom is fixed one naturally obtains the standard Lorenz gauge condition on
$A_{\mu}$, and Maxwell equations in that gauge. This construction has a direct
generalization to arbitrary integer values of $\alpha$, and we comment on the
physically interesting case of linearized Einstein gravity ($\alpha =2$).
