CPT-even}_{\rm lepton} =
        - \frac{1}{2} \overline{\psi} \sigma^{\mu \nu} H_{\mu \nu} \psi
        + \frac{1}{2} \overline{\psi}
            i \gamma^{\mu} c_{\mu \nu} \overset{\leftrightarrow}{D^{\nu}} \psi
        + \frac{1}{2} \overline{\psi}
            \gamma^{5} i \gamma^{\mu} d_{\mu \nu} \overset{\leftrightarrow}{D^{\nu}} \psi,$$

$$\label{theory_L_odd_lepton}
    {\cal L}^{\rm CPT-odd}_{\rm lepton} =
        - \overline{\psi} \gamma^{\mu} a_{\mu} \psi
        - \overline{\psi} \gamma^{5} \gamma^{\mu} b_{\mu} \psi,$$

$$\label{theory_L_even_photon}
    {\cal L}^{\rm CPT-even}_{\rm photon} =
        -\frac{1}{4} (k_{F})_{\alpha \beta \mu \nu} F^{\alpha \beta} F^{\mu \nu},$$

$$\label{theory_L_odd_photon}
    {\cal L}^{\rm CPT-odd}_{\rm photon} =
        \frac{1}{2} (k_{AF})^{\alpha} \varepsilon_{\alpha \beta \mu \nu} A^{\beta} F^{\mu \nu}.$$

The dimensionless coefficients $ c_{\mu \nu} $, $ d_{\mu \nu} $, $ (k_{F})_{\alpha \beta \mu \nu} $ and the coefficients $ H_{\mu \nu} $, $ a_{\mu} $, $ b_{\mu} $, $ (k_{AF})_{\alpha} $ with dimensions of mass are the tensor parameters independent of the space-time coordinates $ x^{\mu} $, encoding the information relevant to the Lorentz invariance violation for physical particles in any given reference frame (for further details see [@sme_theory], [@sme_reviews] and other reviews of the SME).

At present, most of the coefficients describing Lorentz invariance violation in the extended QED have been tightly constrained from the existing experimental data, including that of the experiments aimed at the search of the essentially new phenomena mentioned in the Introduction [@sme_reviews]. The bounds available 