  A simple model is constructed which allows to compute modified dispersion
relations with effects from loop quantum gravity. Different quantization
choices can be realized and their effects on the order of corrections studied
explicitly. A comparison with more involved semiclassical techniques shows that
there is agreement even at a quantitative level.
  Furthermore, by contrasting Hamiltonian and Lagrangian descriptions we show
that possible Lorentz symmetry violations may be blurred as an artifact of the
approximation scheme. Whether this is the case in a purely Hamiltonian analysis
can be resolved by an improvement in the effective semiclassical analysis.
