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., $[x_\mu, x_\nu] \neq 0$ 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.