  The relation between the violation of Lorentz invariance and the dynamical
effects in high energy gamma rays production is discussed. By using the
framework of noncommutative classical electrodynamics, it is shown that full
dynamical calculations are required to put bounds on the Lorentz violating
scale by the phenomenological analysis of these processes as, for example, the
synchrotron radiation from the CRAB nebula. It is observed that an improvement
of the present bound on the scale of noncommutativity can be obtained only by
astrophysical observations of gamma ray spectra in strong magnetic fields such
as pulsars.
