Potential Scattering in Dirac Field Theory

TL;DR

This paper develops a perturbative approach to potential scattering for Dirac spinors, generalizing quantum mechanical results to arbitrary potentials and providing a framework for relativistic scattering analysis.

Contribution

It introduces a perturbation field theory method for Dirac fields that extends quantum mechanical potential scattering to relativistic quantum field theory.

Findings

Reproduces quantum mechanical diffusion results up to second order

Generalizes potential scattering to arbitrary potential forms in Dirac theory

Provides a relativistic framework for potential scattering analysis

Abstract

We develop the potential scattering of a spinor within the context of perturbation field theory. As an application, we reproduce, up to second order in the potential, the diffusion results for a potential barrier of quantum mechanics. An immediate consequence is a simple generalization to arbitrary potential forms, a feature not possible in quantum mechanics.