Radiative Corrections to the Aharonov-Bohm Scattering

TL;DR

This paper calculates the first-order radiative corrections to Aharonov-Bohm scattering of relativistic electrons, revealing an induced magnetic field outside the flux tube and providing a finite, corrected scattering cross section.

Contribution

It introduces the first-order radiative correction to Aharonov-Bohm scattering and demonstrates the generation of an induced magnetic field outside the flux tube.

Findings

First-order radiative correction computed for Aharonov-Bohm scattering.

Second order Born amplitude found to vanish.

Finite inclusive cross section including soft photon effects.

Abstract

We consider the scattering of relativistic electrons from a thin magnetic flux tube and perturbatively calculate the order $\alpha$, radiative correction, to the first order Born approximation. We show also that the second order Born amplitude vanishes, and obtain a finite inclusive cross section for the one-body scattering which incorporates soft photon bremsstrahlung effects. Moreover, we determine the radiatively corrected Aharonov-Bohm potential and, in particular, verify that an induced magnetic field is generated outside of the flux tube.