Spin dynamics in the Frenkel model with allowance for the variation of the inertial properties of the electron

The equations of motion of the Frenkel model $\gamma\gg 1$, $a_{e}\lesssim \chi\ll 1$ (where $\gamma$ is the Lorentz factor, $a_{e}=\frac12 (g-2)$, and $\chi=\sqrt{(eF_{\mu\nu}p_{\nu})^{2}}/m_{e}^{3}$) result in the generalization of the Lorentz and Bargmann–Michel–Telegdi equations. The modification is due to the Frenkel addition $m_{\text{Fr}}$ to the mass of the electron and can be of interest for currently planned experiments with relativistic beams. The derived Frenkel–Bargmann–Michel–Telegdi equation contains a longitudinal part with a time-dependent coefficient, which is nonzero at $g=2$. In the case of constant background fields, the equations of trajectory and spin can be integrated with a required accuracy if the antiderivative of the function $m_{\text{Fr}}(\tau)$ is known. A new representation of the spin-orbit contribution $\Delta m_{so}$ to the mass shift has been found in terms of the geometric invariants of world lines. It has been shown that the rate of variation of $\Delta m_{so}$ is determined by $a_{e}+m_{\text{Fr}}/m_{e}$. The possibility of the periodic variation of spin light along the trajectory of beam has been indicated.