  The unitary representations of the Poincare group of a discrete space-time
are constructed, following the Wigner method in continuum relativity. They can
be interpreted as elementary particles with one significant new feature: the
momentum space being the 4-torus is identified as the Brillouin zone of
space-time where all physical phenomena occur. Consequently 4-momentum is
defined and conserved only modulo a reciprocal lattice vector of the order of
the Planck mass, implying that there is no notion of an invariant mass except
when it vanishes. In particular the propagation of massive particles have
superluminal phases under very large (trans-Planckian) boosts. This behaviour
leads to new features in early cosmology which are not in conflict with current
knowledge.
