Recoil effects and quantum corrections in the semiclassical theory of synchrotron radiation

In a linear approximation with respect to the spin and quadrativ with respect to the recoil parameter, we obtain quantum corrections to the power of synchrotron radiation of an electron. The spin correction is equal to $\xi \zeta$, and the first and second (boson) corrections are $(55\sqrt{3/24})\xi$ and $(56/3)\xi ^2$.