  The lattice of integral points of 4-dimensional Minkowski space, together
with the inherited indefinite distance function, is considered as a model for
discrete space-time. The Lorentz and Poincare groups of this discrete
space-time are identified as subgroups of the corresponding Lie groups. The
lattice Lorentz group has irreducible projective (including linear)
representations which are restrictions of (all) finite-dimensional irreducible
projective representations of the Lorentz Lie group and hence can be used to
describe all integral and half-odd-integral helicity. The (4-torus) momentum
space has a well-defined ``light cone'' of null points and there are orbits of
the lattice Lorentz group lying entirely in the torus light cone and having the
lattice euclidean group of the plane as little group. Wigner's method for the
Poincare Lie group can then be adapted to show, in the first instance, that the
lattice Poincare group has unitary representations describing lattice free
fields of zero mass and an arbitrary Lorentz helicity, in particular chiral
fermions. There are no representations with a nonzero invariant mass.
