Induced representations of Poincare group on the lattice: spin 1/2 and 1   case
  Following standard methods we explore the construction of the discrete Poincare group, the semidirect product of discrete translations and integral Lorentz transformations, using the Wigner-Mackey construction restricted to the momentum and position space on the lattice. The orbit condition, irreducibility and assimptotic limit are discussed. 
M. Lorente, P. Kramer