Exact solutions of the Dirac equation and induced representations of the Poincare group on the lattice

We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincare group on the lattice reveals that they are reducible, a result that can be considered a group theoretical approach to the problem of fermion doubling.