  Starting from an heuristic approach to the semiclassical limit in loop
quantum gravity, the construction of effective Hamiltonians describing Planck
length corrections to the propagation of photons and spin 1/2 fermions, leading
to modified energy-momentum relations, is summarized. Assuming the existence of
a privileged reference frame, we also review the determination of stringent
bounds upon the parameters labelling such corrections, based upon already
existing experimental data, which are found to be from five to nine orders of
magnitude below the expected values.
