  In this paper we make attempt to obtain a description of the Quantum Hall
Effect (both integer and fractional) by means of electron's Green functions of
three-dimensional (planar) electrodynamics. We show that expression for the
free electron propagator yields an integer number for the second Chern-Simons
term, that corresponds to the quantized Hall conductivity in the approximation
of non-interacting particles for integer filling factors, when there exists a
gap for all excitations in the system. Then we try to check correspondence
between fractional case and "interacting" Green functions, so it requires
taking into consideration "full-fledged" propagators, including interactions.
We are going to obtain them from Dyson-Swinger equations. We attempt to reach
out from the perturbation theory regime using a specific method, called scale
approximation. Our solutions are found in general gauge.
