Derivation of the Deformed Heisenberg Algebra from Discrete Spacetime

In this letter, we analyze low energy implications of discrete spacetime, which is motivated from quantum gravity. We first investigate the effects of leading order Planckian lattice corrections on the deformation of the low energy effective Heisenberg algebra. Then we study the corrections to such an algebra from higher order Planckian lattice corrections. These include quantum gravitational terms, which break the rotational symmetry. Finally, we propose a similar deformation of the covariant form of the Heisenberg algebra using a four dimensional Euclidean lattice.