Noncommutative field theory approach to the fractional quantum Hall effect with the filling factor one-half

The fractional quantum Hall effect is studied in the context of the noncommutative quantum field theory in (2+1) dimensions. For the filling factor v = 1/2, the noncommutative effective field theory incorporates a Chern-Simons gauge field (in the temporal gauge) coupled to the matter in the presence of a suitable quenched external magnetic field. After providing the Feynman rules for this system, the noncommutative corrections to the self-energy of quasiparticles are computed, showing that it is zero at Hartree-Fock approximation. Finally, in this approach it is proved that the density p satisfies a noncommutative deformation of the w(infinity)-algebra.