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We consider the theory of spinor fields written in polar form, that is theform in which the spinor components are given in terms of a module times acomplex unitary phase respecting Lorentz covariance. In this formalism, spinorscan be treated in their most general mathematical form, without the need torestrict them to plane waves. As a consequence, calculations of scatteringamplitudes can be performed by employing the most general fermion propagator,and not only the free propagator usually employed in QFT. In this article, weuse these quantities to perform calculations in two notable processes, theelectron-positron and Compton scatterings. We show that although themethodology differs from the one used in QFT, the final results in the twoexamples turn out to give no correction as predicted by QFT.

Cross section for Bhabha and Compton scattering beyond quantum field theory