  We study the Green's function of the $ \nu=1/2 $ Chern-Simons system in the
temporal (Weyl) gauge. We derive the Chern-Simons path integral in the temporal
gauge. In order to do this, we gauge transform the path integral in the Coulomb
gauge which represents the partition function of the correct normal ordered
Chern-Simons Hamiltonian. We calculate the self energy of this path integral in
the random-phase approximation (RPA) for temperature $T=0 $. This self energy
does not have the divergence with the logarithm of the area, which is known to
imply the vanishing of the exact Green's function in the Coulomb gauge for an
infinite area. By Chern-Simons retransforming the path integral representing
the Green's function in the temporal gauge we calculate explicitly the exact
Green's function under the neglection of the interaction between the electrons,
getting a finite value. Furthermore, we give arguments that the Green's
function of the interacting system is also finite. The non-vanishing of the
Green's function for infinite area is due to a dynamical creation of the phase
factors linking the created and annihilated particles with the particles in the
ground state. The absence of these phase factors is the reason for the
vanishing of the Green's function in the Coulomb gauge.
