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Determination of the chemical potential and the energy of the ν=1/2 FQHE system for low temperatures

We consider the energy density of a spin polarized $ν=1/2$ system for low temperatures. We show that due to the elimination of the magnetic field and the field of the positive background charge in the calculation of the grand canonical potential of Chern-Simons systems through a mean field formalism one gets corrections to the well known equations which determine the chemical potential and the energy from the grand canonical potential. We use these corrected equations to calculate the chemical potential and the energy of the $ν=1/2$ system at low temperatures in two different approximations.