Noncommutativity Parameter and Composite Fermions

Abstract

We determine some particular values of the noncommutativity parameter \theta and show that the Murthy-Shankar approach is in fact a particular case of a more general one. Indeed, using the fractional quantum Hall effect (FQHE) experimental data, we give a measurement of \theta. This measurement can be obtained by considering some values of the filling factor \nu and other ingredients, magnetic field B and electron density \rho. Moreover, it is found that \theta can be quantized either fractionally or integrally in terms of the magnetic length l_0 and the quantization is exactly what Murthy and Shankar formulated recently for the FQHE. On the other hand, we show that the mapping of the FQHE in terms of the composite fermion basis has a noncommutative geometry nature and therefore there is a more general way than the Murthy-Shankar method to do this mapping.