Chern-Simons Quantum Field Representation of Planar Ferromagnets

TL;DR

This paper models planar ferromagnets using a Chern-Simons quantum field approach, enabling quantization and revealing potential anyonic excitations with implications for quantum physics.

Contribution

It introduces a novel representation of the 2D Heisenberg spin model as a Chern-Simons gauged nonlinear Schrödinger system, facilitating quantization and analysis of quantum states.

Findings

Quantization of the model achieved via gauge-invariant methods

Preliminary quantum states analyzed and discussed

Physical implications related to anyons explored

Abstract

We represent the two - dimensional planar classical continuous Heisenberg spin model as a constrained Chern-Simons gauged nonlinear Schr\"odinger system. The hamiltonian structure of the model is studied, allowing the quantization of the theory by the gauge invariant approach. A preliminary study of the quantum states is displayed and several physical consequences in terms of anyons are discussed.