Anyon in External Electromagnetic Field: Hamiltonian and Lagrangian Formulations

TL;DR

This paper develops Hamiltonian and Lagrangian formulations for a charged anyon in 2+1 dimensions under electromagnetic fields, revealing a gyromagnetic ratio of two and providing a quantum description of fractional spin particles.

Contribution

It introduces a simple relativistic model for fractional spin particles with electromagnetic interaction, deriving the equations of motion and quantization framework.

Findings

Gyromagnetic ratio for charged anyon is two.

The model satisfies all necessary physical conditions.

Canonical quantization of the system is achieved.

Abstract

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions which satisfies all the necessary conditions. The canonical quantization of the system leads to the description of one- particle states of the Poincare group with arbitrary spin. Using the Hamil- tonian formulation with the set of constraints, we introduce the electro- magnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered in this case.