On the Nonrelativistic Limit of the Scattering of Spin One-half Particles Interacting with a Chern-Simons Field

TL;DR

This paper investigates the nonrelativistic limit of spin-half particle scattering via a Chern-Simons field, revealing magnetic moment effects and divergences managed through automatic counterterms.

Contribution

It provides a detailed one-loop analysis of fermion scattering with Chern-Simons interactions, including vacuum polarization and magnetic moments, with automatic counterterm implementation.

Findings

Magnetic moments for spin up and down fermions are identical.

The scattering amplitude exhibits a logarithmic divergence at high cutoff.

Counterterms are automatically generated without extra assumptions.

Abstract

Starting from a relativistic quantum field theory, we study the low energy scattering of two fermions of opposite spins interacting through a Chern-Simons field. Using the Coulomb gauge we implement the one loop renormalization program and discuss vacuum polarization and magnetic moment effects. We prove that the induced magnetic moments for spin up and spin down fermions are the same. Next, using an intermediary auxiliary cutoff the scattering amplitude is computed up to one loop. Similarly to Aharonov-Bohm effect for spin zero particles, the low energy part of the amplitude contains a logarithmic divergence in the limit of very high intermediary cutoff. In our approach however the needed counterterm is automatically provided without any additional hypothesis.