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.

我们考虑以极坐标形式写的自旋场的理论，即以模数乘以尊重洛伦兹协方差的复数ary相来给出自旋分量的形式。在这种形式主义中，可以将旋转子以其最一般的数学形式来对待，而不必将其限制为平面波。结果，可以通过使用最普通的费米子传播子而不是通常在QFT中使用的自由传播子来执行散射幅度的计算。在本文中，我们使用这些量在两个显着过程中进行计算，即电子-正电子散射和康普顿散射。我们显示，尽管该方法与QFT中使用的方法不同，但两个示例中的最终结果却没有像QFT所预测的那样提供任何校正。