\sim \frac{E}{M_{P}} \, | {\langle}-\gamma^{5} \gamma^{\mu} b_{\mu} {\rangle}| $, and this is also valid for the other appropriate terms in (\[theory\_L\_even\_lepton\])–(\[theory\_L\_odd\_photon\]) as well. Thus, one may neglect the effects caused by non-zero dimensionless Lorentz-violating coefficients in the extended QED when studying the dominant phenomena at feasible energies.

Taken together, the arguments presented above justify the choice of a simplified model (obtained from the extended QED) in which there exists only one type of Lorentz invariance violation described by means of the CPT-odd fermion Lagrangian term $ -{\overline}{\psi} \gamma^{5} \gamma^{\mu} b_{\mu} \psi $ where $ b^{\mu} = \{ b, {\bf 0} \} $. As we believe, this is appropriate for investigating whether $ | b^{0} | $ is indeed much greater than other related parameters of the extended QED by way of studying the characteristics of the synchrotron radiation.

It should be noted, however, that there is an important phenomenon that cannot be neglected in our case when considering the motion of an electron in a magnetic field: Vacuum magnetic moment of the particle. Indeed, provided $ \mu \simeq \mu_{0} \, \frac{e^{2}}{2\pi} $ where $ \mu_{0} = \frac{e}{2m} $ [@Schwinger_vmm], the characteristic energy of the corresponding interaction is $ \mu H 