Representations of the discrete inhomogeneous Lorentz group and Dirac waveequation on the lattice

We propose the fundamental and two-dimensional representation of the Lorent z groups on a (3+1)-dimensional hypercubic lattice, from which representati ons of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transfo rm. From the Dirac representation of the Lorentz group (including reflectio ns) we derive in a natural way the wave equation on the lattice for spin-1/ 2 particles. Finally, the induced representation of the discrete inhomogene ous Lorentz group is constructed by standard methods and its connection wit h the continuous case is discussed.