Consistency of the Born Approximation for the spin-1/2 Aharonov-Bohm Scattering

TL;DR

This paper demonstrates that the Born approximation remains consistent for relativistic spin-1/2 particle scattering in the Aharonov-Bohm effect, confirming its validity up to second order in perturbation theory.

Contribution

It provides a rigorous proof of the consistency of the Born approximation for relativistic spin-1/2 particles in the Aharonov-Bohm scattering scenario.

Findings

First order term matches the exact amplitude expansion

Second order term vanishes, confirming consistency

Supports the validity of the Born approximation in this context

Abstract

The relativistic scattering of a spin-1/2 particle from an infinitely long solenoid is considered in the framework of covariant perturbation theory. The first order term agrees with the corresponding term in the series expansion of the exact amplitude, and second order term vanishes, thus proving that Born approximation is consistent.