Some Comments on the Spin of the Chern - Simons Vortices

TL;DR

This paper calculates the spin of Chern-Simons vortices using a constrained analysis approach, revealing a topological origin for fractional spin and extending the method to non-relativistic models.

Contribution

The paper introduces a method to compute vortex spin in Chern-Simons models and demonstrates its structural invariance across relativistic and nonrelativistic theories.

Findings

Spin formulas are structurally identical in relativistic and nonrelativistic theories.

The topological Chern-Simons term induces fractional spin.

Comparison with existing results confirms the method's validity.

Abstract

We compute the spin of both the topological and nontopological solitons of the Chern - Simons - Higgs model by using our approach based on constrained analysis. We also propose an extension of our method to the non - relativistic Chern - Simons models. The spin formula for both the relativistic and nonrelativistic theories turn out to be structurally identical. This form invariance manifests the topological origin of the Chern - Simons term responsible for inducing fractional spin. Also, some comparisons with the existing results are done.