New approach to quantum corrections in synchrotron radiation. II

Abstract

Continuing our efforts to provide a simple and elegant derivation of a compact (exact) expression for the radiated power of the synchrotron radiation, we here generalize our previous discussion of the radiation by a spin-0 charged particle to that of a spin-\textonehalf{} particle. As in the spin-0 case, we compute the spectrum of the radiated power by using the proper-time method to first calculate the forward Compton scattering amplitude and then apply the optical theorem. The complication due to the inclusion of spin is handled by first decomposing the spin-\textonehalf{} states into the two subspaces of ${\ensuremath{\gamma}}^{0}$, and then using the connection between the two subspaces that is provided by the Dirac equation. Aside from the simple and straightforward operator procedures in computing the result, we also obtain a very simple and compact (one parameter) integral expression for the spectral and angular distribution of the radiated power. Its high-energy, weak-field limit agrees with that obtained from the conventional approach and that from the mass operator method.