  We study the space-time invariances of the relativistic particle action for
both the massive and massless cases. While the massive action has only the
invariances associated to the Poincare algebra, we find that the invariances of
the massless action give rise to the conformal algebra in four dimensions. For
the free massless particle, a new invariance of the action permits the
construction of an extension of the conformal algebra. The conclusion is that
two distinct symmetry breaking mechanisms are necessary to arrive at the
Poincare algebra.
