\sim 10^{-6} \, \text{eV} $ in the typical laboratory field $ H \sim 10^{4} \, \text{gauss} $, so it may be of the same order of magnitude as the quantity $ b^{0} $ (or may be less or greater, the latter being somewhat more likely). Thus, we may not neglect the influence of the vacuum magnetic moment when studying the synchrotron radiation with account of the Lorentz invariance violation in the form we have chosen, and it turns out that the electron vacuum magnetic moment does interact with the condensate $ b_{\mu} $ in a nontrivial way giving rise to the prevailing observable effects (see the main text below).

We have considered the Lagrangian (\[theory\_L\]) in the context of the SME which is based on the conjecture of spontaneous Lorentz symmetry breaking in a more fundamental and profound theory, e.g., string theory (this is the approach generally adopted in [@sme_theory]). At the same time, similar and even the same terms as those present in (\[theory\_L\]) can arise under some other circumstances. In particular, it has been shown [@Kostelecky_liv_grav] that certain weak background effects possible in some generalized theories of gravity should also affect the SME-specific coefficients in (\[theory\_L\_even\_lepton\])–(\[theory\_L\_odd\_photon\]), and concerning 