  In the (2+1)-dimensional QED with and without the Chern-Simons term, we find
the non-local gauge in which there is no wavefunction renormalization for the
fermion in the framework of the Schwinger-Dyson equation. By solving the
Schwinger-Dyson equation in the non-local gauge, we find a finite critical
value $N_f^c$ for the number of flavors $N_f$ of four-component Dirac fermions,
above which the chiral symmetry restores irrespective of presence or absence of
the Chern-Simons term. In the same framework, we study the possibility of
dynamical breakdown of the parity. It is shown that the parity is not
dynamically broken. We discuss this reason from the viewpoint of the
Schwinger-Dyson equation.
