Lattice space-time from Poincaré and κ-Poincaré algebras

Introducing a dimensional parameter κ we propose a realization of the Poincaré and κ-Poincaré algebras by non-local space-time differential operators. The Klein-Gordon and Dirac equations take the form of a finite difference equation. The connection with the deformed Heisenberg algebra is discussed leading to a generalized uncertainty relation.