  We study the simplest geometrical particle model associated with null paths
in four-dimensional Minkowski space-time. The action is given by the
pseudo-arclength of the particle worldline. We show that the reduced classical
phase space of this system coincides with that of a massive spinning particle
of spin $s=\alpha^2/M$, where $M$ is the particle mass, and $\alpha$ is the
coupling constant in front of the action. Consistency of the associated quantum
theory requires the spin $s$ to be an integer or half integer number, thus
implying a quantization condition on the physical mass $M$ of the particle.
Then, standard quantization techniques show that the corresponding Hilbert
spaces are solution spaces of the standard relativistic massive wave equations.
Therefore this geometrical particle model provides us with an unified
description of Dirac fermions ($s=1/2$) and massive higher spin fields.
