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., $[x_{\mu },x_{\nu }]\ne 0$ 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.

Phys.Rev.Lett71(1993)3405. 3pages, LaTeX, IP/BBSR/93-82