Abstract
Owing to a recent controversy over the importance of the second-order quantum corrections to the power spectrum of synchrotron radiation, we here reexamine this question by using a proper time method to calculate the forward Compton scattering of a real photon on a spin-0 charged particle in external magnetic fields. This approach, aside from being the simplest method found so far, has the feature that it resembles the classical procedure so that the quantum corrections can be identified at every stage of the computation. The option of being able to perform first the angular integration before doing the proper time integral enables us to simplify the calculation and to obtain the quantum corrections unambiguously. We find that the criterion for the quantum corrections to be important is the same as that found more than two decades ago.
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