  The quantization of the electromagnetic sector of the Myers-Pospelov model
coupled to standard fermions is studied. Our main objective is to construct an
effective quantum theory that results in a genuine perturbation of QED, such
that setting zero the Lorentz invariance violation (LIV) parameters will
reproduce it. This is achieved by introducing an additional low energy scale
$M$, together with a physically motivated prescription to take the QED limit.
The prescription is successfully tested in the calculation of the electron
self-energy in the one loop approximation. The LIV radiative corrections turn
out to be properly scaled by very small factors for any reasonable values of
the parameters, no fine-tuning problems are found at this stage and the choice
for $M$ to be of the order of the electroweak symmetry breaking scale is
consistent with the stringent bounds for the LIV parameters, in particular with
those arising from induced dimension three operators.
