  We develop a detailed analysis of synchrotron radiation in the effective
Lorentz invariance violating (LIV) model of Myers-Pospelov, considering
explicitly both the dynamics of the charge producing the radiation and the
dynamics of the electromagnetic field itself. Within the radiation
approximation we compute exact expressions in the LIV parameters for the
electric and magnetic fields, the angular distribution of the power spectrum,
the total emitted power in the m-th harmonic and the polarization. We also
perform expansions of the exact results in terms of the LIV parameters to
identify the dominant effects, and study the main features of the high energy
limit of the spectrum. A very interesting consequence is the appearance of
rather unexpected and large amplifying factors associated with the LIV effects,
which go along with the usual contributions of the expansion parameter. This
opens up the possibility of looking for astrophysical sources where these
amplifying factors are important to further explore the constraints imposed
upon the LIV parameters by synchrotron radiation measurements. We briefly
sketch some phenomenological applications in the case of SNRs and GRBs.
