Comment on "Anyon in an external electromagnetic field: Hamiltonian and Lagrangian formulations"

TL;DR

This paper critiques a recent claim about a Lagrangian for anyons, clarifying inaccuracies and reaffirming established results in the literature on anyon statistics in electromagnetic fields.

Contribution

The authors identify inaccuracies in a recent Lagrangian formulation for anyons and clarify the correct approach, reaffirming existing results.

Findings

Inaccuracies in the recent Lagrangian formulation are corrected.

Established results on anyon statistics are reaffirmed.

The corrected formulation aligns with known literature.

Abstract

In their recent letter, Chaichian et.~al. present a Lagrangian for a massive ($m$) point particle on the plane, with which they claim to realize anyon statistics. However, we find that there are some inaccuracies in their formulation and, when these are taken care of, well-known results are reproduced, which already exist in the literature.