The asymptotic behaviour of the exact and approximative ν=1/2\nu=1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the $\nu=1/\tilde{\phi}$ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all $\tau$ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of Hartree-Fock the Green's function corresponds well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function.Comment: 12 Revtex pages, 1 eps figure, using style files pst-feyn.sty, pst-key.sty, typos correcte

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

We consider the energy density of a spin polarized $\nu=1/2$ 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 $\nu=1/2$ system at low temperatures in two different approximations.Comment: 9 Revtex pages, 1 eps figure, using style files pst-feyn.sty, pst-key.sty, typos corrected, one subsection adde