Cross section for Bhabha and Compton scattering beyond quantum field theory

TL;DR

This paper explores Bhabha and Compton scattering using a polar form of spinor fields, demonstrating that the results align with standard quantum field theory predictions without additional corrections.

Contribution

It introduces a formalism for spinor fields in polar form allowing general calculations of scattering amplitudes beyond traditional QFT methods.

Findings

Results match standard QFT predictions

No additional corrections found beyond QFT

Method allows more general spinor treatment

Abstract

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