Non-Abelian Aharonov-Bohm Scattering of Spin 1/2 Particles

TL;DR

This paper investigates the scattering behavior of spin 1/2 fermions with isospin 1/2 in a non-Abelian Chern-Simons field, calculating one-loop amplitudes in both relativistic and nonrelativistic regimes.

Contribution

It provides the first detailed one-loop calculation of non-Abelian Aharonov-Bohm scattering for fermions, including relativistic effects and a novel cutoff method for separating momentum regions.

Findings

Calculated one-loop scattering amplitudes for non-Abelian Aharonov-Bohm effect.

Incorporated relativistic effects such as vacuum polarization and magnetic moments.

Developed a cutoff procedure to handle high and low momentum contributions.

Abstract

We study the low energy regime of the scattering of two fermionic particles carrying isospin 1/2 and interacting through a non-Abelian Chern-Simons field. We calculate the one-loop scattering amplitude for both the nonrelativistic and also for the relativistic theory. In the relativistic case we introduce an intermediate cutoff, separating the regions with low and high loop momenta integration. In this procedure purely relativistic field theory effects as the vacuum polarization and anomalous magnetic moment corrections are automatically incorporated.