# 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.

## Key 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.