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

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., $[x_μ, x_ν] \neq 0$ while a correct treatment would give $[x_μ, x_ν] = 0$. Moreover, their assertion about $α$ being an arbitrary constant in $S_μ= -αp_μ/{\sqrt{p^2}} $ is not correct and consequently one can not say whether the model describes anyons.