Electromagnetic Interaction of Anyons in Non-Relativistic Quantum Field Theory

TL;DR

This paper derives a non-relativistic quantum field theory Lagrangian for anyons interacting with electromagnetic fields, revealing new spin-dependent interactions and confirming known quantum mechanical results.

Contribution

It introduces a novel non-relativistic Lagrangian incorporating non-minimal couplings and spin interactions for anyons in electromagnetic fields.

Findings

Electromagnetic gyromagnetic ratio 2 for any spin

Spin-dependent contact interactions between anyons

Spin dependence of the electromagnetic effective action

Abstract

The non-relativistic quantum field theoretic lagrangian which describes an anyon system in the presence of an electromagnetic field is identified. A non-minimal magnetic coupling to the Chern-Simons statistical field as well as to the electromagnetic field together with a direct coupling between between both fields are the non-trivial ingredients of the lagrangian obtained from the non-relativistic limit of the fermionic relativistic formulation. The results, an electromagnetic gyromagnetic ratio 2 for any spin together with a non-trivial dynamical spin dependent contact interaction between anyons as well as the spin dependence of the electromagnetic effective action, agree with the quantum mechanical formulation.