Perturbation Theory and the Aharonov-Bohm Effect

TL;DR

This paper revisits the perturbation theory expansion of the Aharonov-Bohm scattering amplitude, providing a unified approach for particles with different spins and considering a finite-radius flux line that shrinks to zero.

Contribution

It introduces a unified perturbation theory framework for the Aharonov-Bohm effect with finite-radius flux lines, reconciling previous subcases and extending the analysis.

Findings

Agreement with earlier results on the Aharonov-Bohm effect

Unified treatment of different particle spins

Method handles finite-radius flux lines effectively

Abstract

The perturbation theory expansion of the Aharonov-Bohm scattering amplitude has previously been studied in the context of quantum mechanics for spin zero and spin-1/2 particles as well in Galilean covariant field theory. This problem is reconsidered in the framework of the model in which the flux line is considered to have a finite radius which is shrunk to zero at the end of the calculation. General agreement with earlier results is obtained but with the advantage of a treatment which unifies all the various subcases.