Comment on 'Anyon in External Elecromagnetic Field: Hamiltonian and Lagrangian Formulation'

TL;DR

This paper critiques a recent study on anyons in electromagnetic fields, highlighting errors in the quantization procedure and clarifying the correct geometric and physical properties of the model.

Contribution

It provides a corrected analysis of the Dirac quantization for anyons, clarifying misconceptions and correcting the geometric and physical interpretations in previous work.

Findings

Incorrect noncommutative geometry in the previous model

Proper treatment shows commutative position operators

Questioning the claim about arbitrary constant  in the model

Abstract

We point out that in a recent paper by Chaichian et al. (Phys. Rev.Lett71(1993)3405) Dirac quantization procedure is not properly followed as a result of which the resulting quantum theory is different from what one will get by a straightforward application of Dirac's formulation. For example at quantum level the model in I has noncommutative geometry, i.e., $[x_\mu, x_\nu] \neq 0$ while a correct treatment would give $[x_\mu, x_\nu] = 0$. Moreover, their assertion about $\alpha$ being an arbitrary constant in $S_\mu = -\alpha p_\mu /{\sqrt{p^2}} $ is not correct and consequently one can not say whether the model describes anyons.